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The componentwise stability is a special type of asymptotic stability which ensures the individual monitoring of each state-space variable of a dynamical system. For an interval Hopfield neural network (IHNN), sufficient conditions are provided to analyze the absolute componentwise stability with respect to a class of activation functions (CAF). Both continuous- and discrete-time dynamics are considered. The conditions are formulated in terms of Hurwitz/Schur stability of a test matrix built from the information about the CAF and the interval matrices defining the IHNN. Some interesting results are derived as particular cases, which allow comparisons with several other works.