That is the beginning of black beard/hair algae (BBA for short), or maybe black brush algae. Does it look like fine hair, or is is short and brushy?
It begins this way and then spreads to plant leaves, like you've mentioned. This can be a tough one to control. How strong is your light, and how long do you have it on? BBA happens (there is no scientific proof however), when your light is strong and the nutrients in your water are high. If you have live plants in there, they are so busy processing all the light that the water is deficient of CO2.
It's a tough one to remove...a peroxide dip works IME. You may want to reduce the time your light is on and up your water changes. I guess it's just like many other algae in that respect.
Some fancypants people use flourish excel to help supplement the CO2, but that's only for serious planted tank people, as excel is a little bit dangerous.