We describe Young's mode resonant bar results obtained under effective pressure at two saturation states: dry and water saturated. We monitor primary manifestations of nonlinear response in these experiments: the harmonic content, the source extinction intensity, and fundamental resonant frequency shift. In addition, we describe the hysteretic behavior of the static pressure response, the linear modulus, and Q. Because we currently lack a complete theoretical description of nonlinear behavior under resonance at pressure, we provide relative measures of nonlinear response rather than absolute values. The rocks include Fontainebleau and Meule sandstones and Lavoux limestone. Dynamic strain levels range from 10-8 to 10-5 and frequencies range from 1 to 10 kHz. The elastic nonlinear response of each of the rocks is markedly different over the range of physical property states explored. The different responses are related to differences in mechanical response resulting from rock type, grain cement type, etc. In all of the samples studied, the change in resonant frequency as a function of excitation intensity is not measurable above approximately 10 MPa; however, harmonics are observed at larger effective pressure levels. Hysteresis in velocity and Q versus pressure vary considerably between the rocks. The effect of Q on the experiments is marked. When Q is low (<10) as for some saturated samples, relative excitations must be large in order to induce equivalent dry sample strains.¿ 1997 American Geophysical Union