  We prove a covariant version of the KSGNS (Kasparov, Stinespring,
Gel'fand,Naimark,Segal) construction for completely positive linear maps
between locally $C^{*}$-algebras. As an application of this construction, we
show that a covariant completely positive linear map $\rho $ from a locally
$C^{*}$-algebra $A$ to another locally $C^{*}$ -algebra $B$ with respect to a
locally $C^{*}$-dynamical system $(G,A,\alpha)$ extends to a completely
positive linear map on the crossed product $A\times_{\alpha ^{{}}}G$.
