************************************************************************* 51117 ASCA observations have been extremely powerful in discovering low-Lx active nuclei in a large number of spiral galaxies. The most spectacular example is for the Sbc galaxy NGC 4258: water maser measurements indicated the presence of a hidden massive black hole (MBH) of 10**7-8 solar masses (Miyoshi et al. 1995) and ASCA promptly discovered a low-Lx nuclear activity in this galaxy (Makishima et al.1994). On the other side, though most giant elliptical galaxies are believed to possess MBHs, nuclear activity is still elusive in these objects. This is a major unresolved puzzle. We propose then to observe the E galaxy NGC 3377 which is suspected to hide a ~10**8 MBH to search for hard X-ray nuclear activity and test current theoretical models like advection-dominated accretion disk models. *************************************************************************