Meromorphic functions with prescribed asymptotic behaviour, zeros and poles and applications in complex approximation We construct meromorphic functions with asymptotic power series expansion in $z^{-1}$ at $\infty$ on an Arakelyan set $A$ having prescribed zeros and poles outside $A$. We use our results to prove approximation theorems where the approximating function fulfills interpolation restrictions outside the set of approximation. Keywords:asymptotic expansions, approximation theoryCategories:30D30, 30E10, 30E15