Dual string pairs with N=1 and N=2 supersymmetry in four dimensions

Based on a simple adiabatic argument and by considering the heterotic string counterpart of certain symmetries of Type II superstrings such as (-1)^{F_L} and orientation reversal, we construct orbifold candidates for dual pairs of heterotic and Type II string theories with N=2 and N=1 supersymmetry. We also analyze from a similar point of view the {\rm K3} fibrations that enter in recently proposed N=2 candidates and use this structure together with certain orientation-reversing symmetries to construct N=1 dual pairs. These pairs involve generalizations of Type I vacua which can be equivalent to E_8\times E_8 heterotic strings, while standard Type I vacua are related to SO(32)