Performance analysis of identification methods is the important and difficult projects in the area of system identification.Once one new identification method is born,its convergence analysis appears.The auxiliary model identification is a branch of system identification and has become a large family of identification methods,their convergence brings many projects.This paper studies the consistent convergence of the auxiliary model (AM) based stochastic gradient (SG) algorithm,the AM recursive least squares (RLS) algorithm,the AM multi-innovation SG algorithm,the interval-varying AM SG algorithm and the interval-varying AM RLS algorithm for output-error systems,and analyzes approximately the convergence of the AM recursive generalized extended least squares algorithm for Box-Jenkins systems.