  Coalescing compact star binaries are expected to be among the strongest
sources of gravitational radiation to be seen by laser interferometers. We
present calculations of the final phase of inspiral of equal mass irrotational
neutron star binaries and strange quark star binaries. Six types of equations
of state at zero temperature are used - three realistic nuclear equations of
state of various softness and three different MIT bag models of strange quark
matter. We study the precoalescing stage within the Isenberg-Wilson-Mathews
approximation of general relativity using a multidomain spectral method. The
gravitational-radiation driven evolution of the binary system is approximated
by a sequence of quasi-equilibrium configurations at fixed baryon number and
decreasing separation. We find that the innermost stable circular orbit (ISCO)
is given by an orbital instability for binary strange quark stars and by the
mass-shedding limit for neutron star binaries. The gravitational wave frequency
at the ISCO, which marks the end of the inspiral phase, is found to be around
1100-1460 Hz for two 1.35 solar masses irrotational strange stars described by
the MIT bag model and between 800 Hz and 1230 Hz for neutron stars.
