The end state of a coalescing binary of compact objects depends strongly on
the final total mass M and angular momentum J. Since gravitational radiati
on emission causes a slow evolution of the binary system through quasi-circ
ular orbits down to the innermost stable one, in this paper we examine the
corresponding behavior of the ratio J/M-2, which must be less than 1(G/c) o
r about 0.7(G/c) for the formation of a black hole or a neutron star, respe
ctively. The results show cases for which, at the end of the inspiral phase
, these conditions are not satisfied. The inclusion of spin effects leads u
s to a study of precession equations valid also for the calculation of grav
itational waveforms.