Let $R$ be a commutative ring with $1\neq0$, $N$ a proper submodule of an $R-$module $M$, and $n$ a positive integer. In this paper, we define $N$ to be an $n-$absorbing primary submodule of $M$ if whenever $a_1\ldots a_nx\in~N$ for $a_1,\ldots ,a_n\in~R$ and $x\in~M,$ then either $a_1\ldots a_n\in(N:_RM)$ or there are $(n-1)$ of the $a_i~'s$ whose product with $x$ is in $M-rad(N)$. A number of results concerning $n-$absorbing primary submodules are given.