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In this article we propose a model for stochastic delay differential equationwith jumps (SDDEJ) in a differentiable manifold $M$ endowed with a connection$\nabla$. In our model, the continuous part is driven by vector fields with afixed delay and the jumps are assumed to come from a distinct source of(c\`adl\`ag) noise, without delay. The jumps occur along adopted differentiablecurves with some dynamical relevance (with fictitious time) which allow to takeparallel transport along them. Using a geometrical approach, in the lastsection, we show that the horizontal lift of the solution of an SDDEJ is againa solution of an SDDEJ in the linear frame bundle $BM$ with respect to aconnection $\nabla^H$ in $BM$.

Stochastic delay differential equations with jumps in differentiable manifolds