In recent experiments on photoionization and electron-atom collisions a great number of photons absorbed or emitted were reported. These experiments justify the consideration of the limit of large n for n-photon processes. In this paper a new approximation scheme is developed, which consists in 1/n expansion for the measured quantities. In particular, a complementary region where the low-frequency approximation is applicable is found. It appears that the Kroll-Watson formula is valid even at the very small initial energy provided that the final one is sufficiently large with respect to the laser photon energy.