Its a weird weed called dodder, Ejassalim. It doesn't make its own food from sunlight, and it doesn't have its own roots, so it's dependent on the plant it wraps around for both food and water. When the seeds sprout, they use the stored food in the seed to grow towards chemical cues that tell them there is a nearby plant. When it starts wrapping around its new host, the stem breaks off at soil level.
If it's only attacking the periphery of the plant, you can sometimes get rid of it by pruning off the affected branches. If it is wrapped around the central stem, remove as much as you can by hand, and daub the stuck on portions with a concentrated solution of ammonium sulphate. Be diligent in inspecting the surrounding soil in the future, since it appears to have set seed, and the seeds can survive in the dormant state for years before sprouting and "looking" for a host.

That sounds horrible.

Thanks for the information tugbrethil. No other way of get rid of them? I have wasted a lot of energy trying to clear them. No matter how hard i try, they will be back in the same plant in 2 days.Most people here recommend to destroy the affected plant and burn them to prevent further spreading.

If you have a lot of plants infested, sometimes it is best to cut your losses, and just destroy them. Remember what I said about the seeds, though.
Linda, I suspect a few "B" movies have been based on it! :O