The results of Chow, Moriguti, Robbins and Samuels CMRS 1964 for the secretary problem have been extended to the case with interview costs. Certain tables for chosen cost functions and certain nn denotes the total number of candidates have been provided illustrating the optimal rule and the optimal expected pay-off. A couple of approximations which involve solving differential equations are also given. Next is considered the secretary problem when one can recall the immediately preceding candidate. The optimal rule is derived and is ullustrated for certain cost functions and a few chosen values of n. The approximating differential equations are obtained. The solution to the problem with zero interview cost is obtained.