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This paper introduces new joint estimation methods of multiple carrier frequency offsets (CFOs) and channel impulse responses (CIR) in application to multiuser orthogonal frequency division multiplexing (OFDM) systems. The estimators are derived from the optimal maximum-likelihood (ML) principle. Complexity reductions are achieved by exploiting the correlation properties of the training sequence (TS). The grid search algorithm is converted into a polynomial root finding procedure which leads to low-complexity closed-form estimators for moderate CFOs. Furthermore, iterative estimators for larger CFOs are proposed. Numerical results confirm that the performance degradation due to the approximations compared to the Cramer-Rao bound (CRB) is small and may be negligible in practice.