Abstract The paper considers the recursive identification of Hammerstein systems with noisy output, while its input may or may not be corrupted by noise. The system in the latter case is usually called as EIV system. The conditions required in this paper are considerably weaker than those used in previous works, e.g., the orders of the linear subsystem are allowed to be unknown and no additional conditions are imposed on its moving average part. The nonlinearity is general in the sense that a certain class of functions is out of consideration in some previous papers. In the paper, the almost sure convergence together with convergence rate are established for the estimates for coefficients of the linear part, and then the almost sure convergence for the estimates for the nonlinearity at any given points are derived by using kernel functions. The convergence rate for the nonlinearity is also obtained for the case where the system input is available without noise. A numerical example is provided, and the simulation results are consistent with the theoretical analysis.