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This paper investigates reconfigurable intelligent surface (RIS)-assisted secure multiuser communication systems in the presence of hardware impairments (HIs) at the RIS and the transceivers. We jointly optimize the beamforming vectors at the base station (BS) and the phase shifts of the reflecting elements at the RIS so as to maximize the weighted minimum approximate ergodic secrecy rate (WMAESR), subject to the transmission power constraints at the BS and unit-modulus constraints at the RIS. To solve the formulated optimization problem, we first decouple it into two tractable subproblems and then use the block coordinate descent (BCD) method to alternately optimize the subproblems. Two different methods are proposed to solve the two obtained subproblems. The first method transforms each subproblem into a second order cone programming (SOCP) problem by invoking the penalty convex–concave procedure (CCP) method and the closed-form fractional programming (FP) criterion, and then directly solves them by using CVX. The second method leverages the minorization-maximization (MM) algorithm. Specifically, we first derive a concave approximation function, which is a lower bound of the original objective function, and then the two subproblems are transformed into two simple surrogate problems that admit closed-form solutions. Simulation results verify the performance gains of the proposed robust transmission methods over existing non-robust designs. In addition, the MM algorithm is shown to have much lower complexity than the SOCP-based algorithm.