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Reactivity is an essential property of a synchronous program. Informally, it guarantees that at each instant the program fed with an input will"react" producing an output. In the present work, we consider a refined property that we call feasible reactivity. Beyond reactivity, this property guarantees that at each instant both the size of the program and its reaction time are bounded by a polynomial in the size of the parameters at the beginning of the computation and the size of the largest input. We propose a method to annotate programs and we develop related static analysis techniques that guarantee feasible reactivity for programs expressed in the SΠ-calculus. The latter is a synchronous version of the Π-calculus based on the SL synchronous programming model.