The author studies the stochastic differential inclusion \[ du(t)+A(t,u(t))\,dt+C(u(t))\,dt+B(t,u(t))\,dw(t)\ni O,\quad u(0)=u_ 0, \tag{1} \] where \(A: \Omega\times [0,T]\times \mathbb R^ d\to \mathbb R^ d\), \(C\) is a maximal monotone set-valued map from \(\mathbb R^ d\) into \(\mathbb R^ d\), and \(B: \Omega\times [0,T]\times \mathbb R^ d\to \mathcal L(\mathbb R^ d)\). He gives conditions under which this differential inclusion has a unique continuous solution. In the proof of the existence theorem he approximates the inclusion (1) by stochastic differential equations \[ du(t)+[A(t,u(t))+C_ n(u(t))]\,dt+B(t,u(t))\,dw(t)=0,\quad u(0)=u_ 0, \] where \(C_ n\) are Yosida approximations of \(C\). He proves that the sequence \(\{u_ n:n\in\mathbb N\}\) of solutions of these equations is a Cauchy sequence, and the limit process is a solution of (1).