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Abstract. The existence of a capacity solution to a coupled nonlinear parabolic-elliptic system is analyzed, the elliptic part in the parabolic equation being of the form − div a (x, t, u, ∇u). The growth and the coercivity conditions on the monotone vector field a are prescribed by an N -function, M , which does not have to satisfy a Δ2 condition. Therefore we work with Orlicz-Sobolev spaces which are not necessarily reflexive. We use Schauder's fixed point theorem to prove the existence of a weak solution to certain approximate problems. Then we show that some subsequence of approximate solutions converges in a certain sense to a capacity solution.Mathematics Subject Classification. 35K60, 35D05, 35J70, 46E30.

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