Abstract: To investigate a special type of set-valued stochastic functional differential equations which drift coefficient is set-valued stochastic process and diffusion coefficient is single-valued stochastic process,the definition of solutions for this type of equations was introduced,and its existence and uniqueness theorem of solutions was proved under the Lipschitz and linear growth conditions.Set-valued stochastic differential delay equations also were discussed,and in order to develop its applications,the Caratheodary approximate solutions were given.