The random convex analysis of subdifferentials and approximate subdifferentials is carried out in this paper. Based on the analysis of the stratification structure and the recently developed separation theorems in random locally convex modules, some nice basic properties about subdifferentials and approximate subdifferentials of a L⁰-valued function on random locally convex modules are obtained. The main results are as follows. First, for a proper and T_c-lower semicontinuous L⁰-valued L⁰(F)-convex function f defined on a random locally convex module (E, Λ) where both E and Λ have the countable concatenation property, it is proven that the approximate subdifferential of f is nonempty. Second, for two propers and T_c-lower semicontinuous L⁰-valued L⁰(F)-convex functions, denoted by f and g, which are defined on a random locally convex module (E, Λ) where both E and Λ have the countable concatenation property, the formula about the subdifferentials of f+g is given.