Stochastic delay differential equations (SDDE) on a manifold M depend intrinsically on a connection del in this space. The main geometric result in this notes concerns the horizontal lift of solutions of SDDE on a manifold M to an SDDE in the frame bundle BM, hence the lifted equation should come together with the prolonged horizontal connection del(H) on BM. We show that every horizontal semimartingale can be represented as a solution of an SDDE.10190195