Probably hair algae from the description. Near impossible to eradicate in my experience. You can remove it by hand (or by twirling a toothbrush through it) if your plants are not too delicate. It always grows back though. Try adding a rapid growing plant like hornwort which may out-compete the algae for nutrients. Less light may help, it does with alot of algae types. One of my tanks has hair algae, the other green slime stuff and I'd rather have hair algae than the truely unsightly slime! Incidently it is not a problem having algae, but it can be unsightly.