No, you can't. If its planted on your neighbour's land and not yours, there's nothing you can do about it. If you're at all friendly with them, you might ask how they're intending to grow it - kept pollarded or stooled, it'll be fine, but left to grow untrammelled, it will be very large indeed, over 65 feet, with roots which reach down to the water table (it's the deepest rooting tree in the world). It's growth rate is about 6 feet a year, so quite a fast grower. Even so, you have no power over what they do or don't do with it, other than the legal right to remove any parts which overhang the boundary into your land back to the boundary only, not over into theirs. And even then, those cuttings are technically theirs, not yours, so should be offered back to them after cutting.

That's outrageous! SURELY there's something that can be done? Even the threat of their liability to pay you damages when their roots cause your house to collapse?

Agree with Bamboo, even an apple hanging over your fence is not yours. Deplomacy is the easiest answer.
You do have rights to the soil on your side, so whilst it is small, a barrier to prevent root growth on your side and when it grows big enough it will fall away from your house (given the right gust from your side) and you will have less roots going your way to affect your foundations.
Another thought, aren`t you allowed to use chemical weedkillers on anything that is in your garden? If it does grow into your space couldn`t you zap it? (I don`t know `cos I never use the stuff but i`m sure there is a chemical out there, monsanto must be researching past roundup now?)
Sorry - on a rant, but maybe others might know the legality of using weedkillers on plants that invade your boundries?

A root barrier would sound like a good idea only if I didn't have to dig up my entire cemented paved path at the side of the house!

My neighbour is being unreasonable and unfortunately he's decided to fall out with me for trying to stop him so diplomacy has already failed! I think the guy has problems but thats another story.

Gattina - Yes I was thinking that maybe I could claim for damages against his house insurance if (when) his tree begins to cause structural and drainage problems on my side!

This is an aweful situation, not least because I'm now made into an enemy with him!

To quote Jean-Paul Sartre, "Hell is other people!" I suppose in a way, if you've already fallen out, it clears the way for a few home truths and veiled threats about the liability. Terrible situation: you have my sympathy. I wish I knew more about the law.
Our first home was in a pretty little private close in Harrow, with a beautiful avenue of horse chestnut trees leading to it. Next to this avenue was an old house, which was bought by a developer, and one day we came home to find every tree had been felled, with no notice. We were incensed, and discovered the developer had sent someone onto our land to chop them down. He had, of course, to pay some derisory damages, but nothing was going to restore our lovely trees, and within the year a monstrous block of flats went up, with no danger of the tree roots damaging their foundations. So sad.

We had a back neighbour who put a Rhus tree right near our back fence. After a few years we had shoots coming up everywhere. I treated these patiently over time with a lethal substance and the tree slowly started to fail. He eventually chopped it down. We never said a word. My advice is....keep schtum and do what you must very very discretely indeed. As it is a path, take out a small portion near the tree. Put a gutter pipe down pointing to the boundary.. Cover over the spot, and do what you must to defend your property at discrete intervals. Gums also shed large rolls of bark when mature. Presumably you would sling those back as well!!!

Brilliant, Dorjac.

Unfortunately, the roots on Eucalyptus tend to go straight down, and for a long way, so any interference at root level will probably have no impact whatsoever. Equally, spraying or treating a neighbour's plant, even on your overhanging parts, is illegal if its likely to kill or damage the plant. In fact, it's illegal to spray or use any pesticide or herbicide on anything other than your own land, and that includes the bit where your front path meets the street paving, a spot where weeds often arise.
I would, though, take photographs, preferably with a date, and keep them for later reference in case of any claim you need to make. Certainly, if the tree causes subsidence or drain problems, any roots found to be the cause should be sent to a laboratory for identification - if it turns out to be the neighbour's tree, they're liable for the costs of repairing the damage. Usually, the insurance company will carry out this investigation.

Let's hope the neighbour plans to keep it stooled!

THEIR insurance company? If (heaven forbid) it comes to that, I'd get your own professional, disinterested survey done, or get your own insurance company's report.

No, Gattina - if your house is affected by subsidence, or the drains are damaged, and you're insured (building insurance), it's your own insurers who should investigate the cause. They don't want to pay any more than you do...

if this tree is proven to dammage your property then they will be held accountable . eucalyptus are one of the tallest trees on the plannet to and on there own can tend to get blown over in strong winds . sorry but as bamboo sais you cant do a thing untill the tree litteraly causes you a problem ie your drainage . untill then youl just have to put up with it . pitty it cant grow the odd root in your garden as trees hate copper as its very subtle and lethal to plants .

I have the same problem. Our neighbor completely ignores the property line. In fact he removed the markers. And has put down stone slabs. He wants the side of the barn(which is his) to be large enough to store his big logs. I would not mind, but the next guy won't like it as he is messy and tends to throw a bit of this and that on top of these logs. He has extended his line width wise all the way to the main street. In addition, has planted daylilies that are marching all over our lawn. How to cope without getting into a big fight? The problem is that we are all very good friends with the wife, and find him impossible. I am going to send him the map from the Town Hall first, I do not want to consult a lawyer...money, money, money.

Any practical ideas on this one?

I should think our boundary laws are different to yours in the USA. Gardens or yards in the USA are more open plan than our tightly fenced little enclaves. I have a vision of him tippy toeing around moving markers while you are away or at 3am in the morning. Maybe you could move them back again to where they were. I suppose, if he gets away with it every time, he thinks he is top dog and no one is going to issue a challenge. Day lillies might get mowed when you are grass cutting? Whoops!!! Oh sorry I thought that was mine to mow.

Not really, but I do know you need to confront the issue of his creeping boundary line - if you don't, after a number of years it will be accepted that the boundary is where he's marked it... I'd dig his stuff out on my side and erect a low fence right on the edge of where you know the boundary should be, or plant a low hedge of some kind. And I'd tell him I was going to do it because I wanted definition of my garden, or some such twaddle, any reasonable excuse you can think of.

I really like your ideas. Especially the lawn mower going over the Day lilies. They are those ugly orange lilies that grow by our roadsides on top of everything else! How can people have such nerve??? Our plot is very small and the houses are very close together. I have considered a fence, but they are very expensive here. They have a driveway that is so narrow they have to back out, and with a fence, they would be completely boxed in. Now they have the luxury of looking down my beautiful garden, free of charge!

It is so infuriating when your neighbour not a considerate person. It seems very strange to us in UK how open folks gardens are in the USA, on all the films we see. I have often wondered how the boundaries are determined.