We analyze the high-order harmonics generation using 1 kHz and 100 kHz lasers by ablating different rotating targets. We demonstrate the high average flux of short-wavelength radiation using the latter laser, while comparing the plasma formation conditions at different pulse repetition rates. The analysis of harmonic stability in the case of the 100 kHz experiments showed the two-fold decay of the 27th harmonic generating in silver plasma after 3.5×106 shots. The advantages of shorter pulse-induced ablation for the improvement of harmonic generation stability are demonstrated. Two-color pump of plasma, resonance enhancement of single harmonic, and quasi-phase matching studies are presented for 1 kHz laser applications. The formation of modulated multi-jet plasma on the plane and curved surfaces during ablation by 100 kHz pulses is demonstrated. In the case of the 25th harmonic of 1030 nm radiation (E=30 eV) generated during experiments in carbon plasma, at 100 kHz and 40 W average power of driving pulses, 0.4 mW of average power for single harmonic in the 40 nm spectral range was achieved.