Could it be a slug or snail trail? If so then you could put slug pellets down. Or maybe there's an organic way? I'm sure someone will be along shortly to give you some more advice.

It sounds like it could be aphids as they suck sap and then leave sticky deposits of it on the leaves.

If you want to get rid of them then you can either get a spray from a diy store or garden centre that targets aphids/greenfly or if you don't want to use proprietory chemicals which are often harmful to beneficial insects such as bees you can spray with diluted soapy water. Someone on here suggested putting nettle leaves in water in a container and covering and leaving for a few days and then spraying the liquid on plants and it apparently worked very well for them. If it the nettles are left longer then it becomes concentrated and you might need to dilute it for spraying on plants.