  We propose a possible resolution for the problem of why the semicircular law
is not observed, whilst the random matrix hypothesis describes well the
fluctuation of energy spectra. We show in the random 2-matrix model that the
interactions between the quantum subsystems alter the semicircular law of level
density. We consider also other types of interactions in the chain- and
star-multimatrix models. The connection with the Calogero-Sutherland models is
briefly discussed.
