  The nonlinear magnetization is considered within the Ginzburg-Landau
theoretical framework, in the Meissner regime. A calculational method in the
case of conventional superconductors (one order parameter) is developed and is
extended for the case of two order parameters (s+d mixing). It is confirmed
that corrections tou the penetration depth, in the mean field analysis, are of
the order of ${H_0}^2$ where $H_0$ is the applied field. We analyze carefully
the possible solutions which lead to different scenarios in the physics of the
symmetry of the order parameter. The anisotropy in the penetration depth is
calculated and the temperature dependence of the magnetization is extracted. We
discuss the relevant experimental results in the light of these calculations.
