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An incremental least‐mean M‐estimate algorithm is proposed for distributed network, which minimises a robust M‐estimator‐based cost function against impulsive noise via the gradient descent method. Moreover, based on the same frame for implementation, an incremental distributed least‐mean p‐power algorithm is presented for combating impulsive noise. Simulations verify the superiority of the proposed algorithms in the presence of impulsive noise relative to some existing incremental distributed algorithms. [ABSTRACT FROM AUTHOR]