The paper deals with a branch in the recursive parametric estimation within stochastic system identification problems, concerned with application of non-vanishing (both scalar-valued and matrix-valued) gain algorithms. Corresponding features of projection recursive algorithms of a general type are examined, and convergence properties are established. A number of simulation results are presented, which confirms the theoretical considerations and inferences. The consideration is supplemented with presentation of a way to decrease the influence of different types of uncertainty and inaccuracy, concerned with both computations themselves and system undermodeling. Corresponding numerical comparison with the recursive least squares technique is also implemented confirming the suitability of the approach proposed.