Summary: We present some new stability results for nonlinear equations with distributed delay \[ \dot x(t)+ \sum^m_{k=1} \int^t_{h_k(t)} f_k(s, x(s))\,d_s R_k(t, s)= 0. \] The results are applied to establish local stability of some models of population dynamics: the Nicholson’s blowflies equation and the Mackey-Glass equation describing white blood cells production.