The author considers a stochastic functional differential equation of the form \[ dD(t,x_t)=f(t,x_t)\,dt+g(t,x_t)\,dw(t). \] Under the condition of uniform stability of the operator \(D\), the author obtains a sufficient condition for the stochastic uniform stability of the solution. He also discusses the stochastic asymptotic stability of stochastic delay equations of the form \[ d[x(t)-G(x(t-\tau))] =f(t,x(t), x(t-\tau))\,dt+g(t,x(t),x(t-\tau))\,dw(t). \]