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Abstract. We prove that if t 7 → u(t) ∈ BV(R) is the entropy solution to a N × N strictly hyperbolic system of conservation laws with genuinely nonlinear characteristic fields ut + f(u)x = 0, then up to a countable set of times {tn}n∈N the function u(t) is in SBV, i.e. its distributional derivative ux is a measure with no Cantorian part. The proof is based on the decomposition of ux(t) into waves belonging to the characteristic families u(t) = N∑ i=