We consider the following stochastic differentic equationwhereZis a given semimartingale andKis a given process with right-continuous and lefthand limited paths, on some filtered probability space. We prove the exixtence of a strong solution (or: solution-process) on this space, under an at most linear growth condition on g, when the usual Lipschitz Countinuity ofg,(ω,x) inxis replaced by weaker hypothese, namely that gs(ω,x) is continuous inxand satisfies a monotonicity condition related to the processZ.