This paper reflects a presentation made at the 16th International Conference on Nonlinear Elasticity in Materials (the XVI ICNEM) held in Prague, Chech Republic, on June 5-11, 2011. It includes an outline of nonlinear dynamical models and experimental facts related to "slow time" phenomena in rock and non-consolidated geomaterials, including our field experiment, where a logarithmic restoration of Rayleigh wave phase velocity was observed. Several simplified models of stress-strain relation in media with relaxation and wave propagation in such media is also considered.