Abstract. The velocity of sound in rock is a strong function of pressure, indicating that wave propagation in rocks is very nonlinear. The quasistatic elastic properties of rocks axe hysteretic, possessing discrete memory. In this paper a new theory is developed, placing all of these properties (nonlinearity, hysteresis, and memory) on equal footing. The starting point of the new theory is closer to a microscopic description of a rock than the starting point of the traditional five-constant theory of nonlinear elasticity. However, this starting point (the number density ρ of generic mechanical elements in an abstract space) is deliberately independent of a specific microscopic model. No prejudice is imposed as to the mechanism causing nonlinear response in the microscopic mechanical elements. The new theory (1) relates suitable stress-strain measurements to the number density ρ and (2) uses the number density ρ to find the behaviour of nonlinear elastic waves. Thus the new theory provides for the synthesis of the full spectrum of elastic behaviours of a rock. Early development of the new theory is sketched in this contribution.