Consider the stochastic differential inclusion \[ (1)\quad du(t)+A(t,u(t))dt+C(u(t))dt+B(t,u(t))dw(t)\ni 0,\quad u(0)=u_ 0, \] where A,B: [0,T]\(\times R\to R\), and C is a maximal monotone set-valued map from R into R. Under some regularity conditions, the author associates with this inclusion the family of ordinary differential equations \[ (2)\quad D_ t'=F(t,D_ t),\quad D_ 0=u_ 0 \] parametrized by \(\omega\) from the base probability space. The function F is expressed by the coefficients of the differential inclusion, the Wiener process w(t), and the function \(h: [0,T]\times R\times R\to R\) satisfying the equation \[ (\partial /\partial \beta)h(t,\alpha,\beta)=- B(t,h(t,\alpha,\beta)),\quad h(t,\alpha,0)=\alpha. \] The author proves that the solvability of the inclusion (1) is equivalent to the solvability of the equation (2) for almost all \(\omega\), and the following relations between their solutions hold: \[ u(t)=h(t,D_ t,w(t)),\quad D_ t=h(t,u(t),-w(t)). \] A related result for stochastic differential equations was obtained by \textit{H. Doss} [Ann. Inst. Henri Poincaré, n. Ser., Sect. B 13, 99-125 (1977; Zbl 0359.60087)]