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In this paper, an iterative learning recursive least squares (ILRLS) identification method is developed by considering a class of repetitive systems. First, considering a repetitive discrete-time system corrupted by white noise, we present a linear time-varying data model to describe the input-output dynamic behavior of the system in iteration domain. On this basis, two ILRLS methods are proposed taking both white noises and colored noises into consideration. With an extensive analysis, the two proposed methods are shown applicable to repetitive nonlinear discrete-time systems owing to their data-driven nature by which no explicit models are required. The proposed ILRLS methods are executed pointwisely along the iteration direction, and they can also deal with time-varying uncertainties. The results are proved and verified by mathematical analysis along with simulations.