The paper presents an approach to derive stochastic approximation type algorithms used within general schemes of system identification. The technique proposed enables one to derive recursive identification algorithms under fairly mild assumptions with respect to noises and disturbances corrupting the observations. For completely unknown disturbance model (as it normally should be), the identification criterion based on the extended overdetermined instrumental variable method is used. The algorithms obtained do not involve inversion of the criterion Hessian, and are stable with respect to variation of the Hessian rank.