Summary: Asymptotic expansions are derived for the Laplace convolution \((f* g)(x)\) as \(x\to\infty\), where \(f\) and \(g\) have asymptotic power series representation in descending powers of \(t\). Bounds are also constructed for the error terms associated with these expansions. Similar results are given for the convolution integrals \[ \int^ \infty_ 0 f(t)g(x+ t) dt\quad\text{and}\quad \int^ \infty_ 0 f(t)g(x- t) dt \] as \(x\to\infty\). These results can be used in the study of asymptotic solutions to the renewal equation and the Wiener-Hopf equations.