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[en] The representation formula for hysteresis operators acting on scalar-valued continuous input functions being piecewise monotone that was derived in Brokate and Sprekels (1996)  has been extended to results for hysteresis operators acting on vectorial input function, see Klein (2012, 2014) [2–5]. In the current paper, the representation result is extended to rate-independent systems, as considered for example in Mielke (2005) . The input functions are requested to be continuous and to be piecewise strictly monotaffine, i.e. to be piecewise the composition of a strictly monotone increasing function with an affine function, the strictly monotone function being applied first.