Static average polarizabilities, alpha, and second hyperpolarizabilities, gamma, of ZnmCdn nanoclusters for m + n = 2 - 6 have been calculated, at the ab initio level, using effective core potentials (ECP). We have developed in a systematic way a series of basis sets. Employing a hierarchy of methods (HF, MP2, CCSD, CCSD(T)), we have computed the polarizability of Cd. The alpha value we computed is in excellent agreement with the best theoretical and experimental values. From the set of the designed basis sets we selected one, for the calculation of the polarizabilities of the considered clusters, which gives a satisfactory alpha value for Cd, at a low computational cost. The basis set for Zn has been reported in our recent study of the properties of Zn-m. We have also employed the basis sets developed by Kello and Sadlej in order to compute the relativistic correction to alpha, which has been compared with the corresponding correlation contribution to alpha of ZnmCdn. We have employed two ECPs, having a small and a large core. The polarizability results for Cd-m, which have been computed by employing them, agree at the HF level, but at the MP2 level have a remarkable difference. The variation of alpha/m as a function of m for Zn-m and Cd-m, has been discussed. The average second hyperpolarizabilities of all clusters, at the MP2 level, are well described by a linear function of the composition of the clusters using constant atomic increments.