a b s t r a c tWe study the structure of tensorial products for the autoregressive and moving average processes (X n ), with values in a Hilbert space H and with innovations that are martingale differences.The obtained models are ARMA(H ⊗ H) processes, possibly non standard. We provide criteria for the standardness of these models, we specify the results in the real case, give some examples and consider some applications.