Building of high average output power excimer lasers requires the solution of several complex problems. The main challenge is the creation of a uniform discharge which can be easily reproduced even at high pulse repetition rates. Some approaches to solving this problem are discussed. They resulted in creation of lasers with aperture of 4 sq cm operating at 1 kHz producing the output of 420 W at 308 nm. A large-aperture XeCl laser can produce 10 J per pulse at 50 Hz.