A variation of the excite-and-probe technique is used to measure the picosecond evolution of laser-induced transient gratings that are produced in germanium by the direct absorption of 40 psec optical pulses at 1.06-μm. Grating lifetimes are determined for free carrier densities between 10¹⁸ cm⁻³ and 10²¹ cm⁻³ . For carrier densities less than 10¹⁹ cm⁻³ , a linear diffusion-recombination model for the grating provides a good fit to the experimental data and allows the extraction of the diffusion coefficient and an estimation of the linear recombination lifetime. Above carrier densities of approximately 10²⁰ cm⁻³ , the density dependence of the diffusion coefficient and nonlinear recombination processes must be considered. Numerical solutions to the resulting nonlinear partial differential equation are obtained that allow extraction of information concerning the high density diffusion coefficient and the nonlinear recombination rates.