In this paper we discuss the concept of weak solution for a new type of mean-field stochastic differential equations,which drift coefficient depends on the full past of the state but also on the law of the solution.With the help of the Girsanov Theorem we prove the existence and the uniqueness in law of the weak solution,when the drift coefficient is a bounded and only measurable function of the solution process and a continuous one of the law of the solution process.In the second part of the work we apply this concept of weak solution to zero-sum stochastic differential games of mean-field type.We obtain for them the existence of generalized saddle point controls under Isaacs' condition and we discuss conditions under which we have saddle point controls.