  We consider initial-boundary problems for general linear first-order strictly
hyperbolic systems with local or nonlocal nonlinear boundary conditions. While
boundary data are supposed to be smooth, initial conditions can contain
distributions of any order of singularity. It is known that such problems have
a unique continuous solution if the initial data are continuous. In the case of
strongly singular initial data we prove the existence of a (unique) delta wave
solution. In both cases, we say that a solution is smoothing if it eventually
becomes $k$-times continuously differentiable for each $k$. Our main result is
a criterion allowing us to determine whether or not the solution is smoothing.
In particular, we prove a rather general smoothingness result in the case of
classical boundary conditions.
