  H-distributions associated to weakly convergent sequences in Sobolev spaces
are determined. It is shown that a weakly convergent sequence $(u_n)$ in
$W^{-k,p}( \R^d)$ has the property that $\theta u_n$ converges strongly in
$W^{-k,p}(\R^d)$ for every $\theta\in\mathcal S(\R^d)$ if and only if all
H-distributions related to this sequence are equal to zero. Results are applied
on a weakly convergent sequence of solutions to a family of linear first order
PDEs.
