It is pretty hard to tell from just a description.  It might be something as simple as a spider which isn’t a problem…just brush the web away.  If it is a denser web then it might be spider mites which can for a web-like structure on the stems.  In that case, spray the plants with Bonide Bon-Neem…an organic spray that is effective against spider mites.    If you can bring a sample in a baggie or some clear pictures of the problem to the gsrden center, they can ID it.