Members of a wide class of geomaterials are known to display complex and fascinating nonlinear and nonequilibrium dynamical behaviors over a wide range of bulk strains, down to surprisingly low values, e.g., 10-7. In this paper we investigate two sandstones, Berea and Fontainebleau, and characterize their behavior under the influence of very small external forces via carefully controlled resonant bar experiments. By reducing environmental effects due to temperature and humidity variations, we are able to systematically and reproducibly study dynamical behavior at strains as low as 10-9. Our study establishes the existence of two strain regimes separated by $epsilon$ M . At strains below $epsilon$ M the material is nonlinear and quasi-equilibrium thermodynamics applies as evidenced by the success of Landau theory and a simple macroscopic description based on the Duffing oscillator. At strains above $epsilon$ M the behavior becomes truly nonequilibrium, as demonstrated by the existence of material conditioning, and Landau theory no longer applies. The main focus of this paper is the study of the first region, but we also comment on how our work clarifies and resolves previous experimental conflicts, as well as suggest new directions of research.