The two-stage stochastic second-order cone programming model has been widely used in many practical problems such as engineering, production, neural networks, and so on. The effective methods of this model have attracted more attention. It is well known that optimality condition plays an important role in algorithm design. Based on Lagrange duality theory, this paper mainly discusses optimality conditions for a two-stage stochastic second-order cone programming problem with general distribution. Firstly, under Slater condition, the dual problem of the second-stage problem is established. Secondly, the sub-differential properties of expected value function of second-stage problem and expected recourse cost function are analyzed. Finally, optimality conditions for the two-stage stochastic second-order cone programming problem with general distribution are developed.

two-stage stochastic second-order cone programming, dual problem, expected recourse cost, optimality condition, general distribution.