The far-infrared magneto-photoconductivity due to optical transitions from the acceptor ground state into quasi-bound Coulomb states in p-Ge has been investigated at low temperatures as a function of intensity applying a high-power cw molecular laser. For intensities above about 1 mW/cm2 the photoconductive signal shows a square root dependence on intensity, which is attributed to nonlinear free carrier capture in the low compensated material. The experimental results are analyzed in terms of a rate equation model yielding the kinetic parameters of the carrier generation- and recombination process involved.