  Let $\mathcal F=(F, +. \cdot, <, 0, 1, \dots)$ be a definably complete
locally o-minimal expansion of an ordered field. We demonstrate the existence
of definable quotients of definable sets by definable equivalence relations
when several technical conditions are satisfied. These conditions are satisfied
when $X$ is a locally closed definable subset of $F^n$ and there is a definable
proper action of a definable group $G$ on $X$.
