  We discuss an approach for studying the properties of mesoscopic systems,
where discrete and continuum parts of the spectrum are equally important. The
approach can be applied (i) to stable heavy nuclei and complex atoms near the
continuum threshold, (ii) to nuclei far from the region of nuclear stability,
both of the regions being of great current interest, and (iii) to mesoscopic
devices with interacting electrons. The goal is to develop a new consistent
version of the continuum shell model that simultaneously takes into account
strong interaction between fermions and coupling to the continuum. Main
attention is paid to the formation of compound resonances, their statistical
properties, and correlations of the cross sections. We study the Ericson
fluctuations of overlapping resonances and show that the continuum shell model
nicely describes universal properties of the conductance fluctuations.
