Sabine, that is one cool tank!
Very nice stand and light fixture too!

What kind is it?
About your question, the best way to get rid of the algae is probably manual removal!
Trim all effected leaves.
To keep it from getting worse or coming back you will have to correct the problem... water parameters.
Can you tell us, PH, KH, GH, NH4, NO2, NO3, PO4 and the size of the tank and how much light?
Good luck