  Let $K/F$ be a quadratic extension of $p$-adic fields, and $n$ a positive
integer. A smooth irreducible representation of the group $GL(n,K)$ is said to
be distinguished, if it admits on its space a nonzero $GL(n,F)$-invariant
linear form. In the present work, we classify genric distinguished
representations of the group $GL(n,K)$ in terms of inducing
quasi-square-integrable representations. This has as a consequence the truth of
the expected equality between the Rankin-Selberg type Asai $L$-function of a
generic representation, and the Asai $L$-function of its Langlands parameter.
