We present a new technique for the numerical detection and
localization of connecting orbits between hyperbolic invariant
sets in parameter
dependent dynamical systems. This method is based on set-oriented multilevel
methods for the computation of invariant manifolds and it can be applied
to systems of moderate dimension. The main idea of
the algorithm is to detect intersections of coverings of the stable and
unstable manifolds of the invariant sets on different levels of the
approximation. We demonstrate the applicability of the new method by
three examples.