[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) [1] 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) [9]. 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.