||In the first part of this paper we have deduced a classification of asymptotic shallow shell models with respect to the level of applied forces, from the non-linear three-dimensional elasticity. We have used a constructive approach based on a dimensional analysis of the non-linear three-dimensional equilibrium equations, which naturally makes appear dimensionless numbers characterizing the applied forces(F and G) and the geometry of the shell (ε and C). To limit our study to one-scale problems, these dimensionless numbers are expressed in terms of the relative thickness ε of the shell, considered as the perturbation parameter. In the first part, we have studied the case of shallow shells corresponding to C=ε2. In the second part of this paper, we will study the case of strongly curved shells for which C=ε. The classification that we obtain is then more complex. It depends not only on the force levels, but also on the existence of inextensional displacements which keep invariant the metric of the middle surface of the shell.