  We critically re-examine the available data on the spectral types, masses and
radii of the secondary stars in cataclysmic variables (CVs) and low-mass X-ray
binaries (LMXBs), using the new catalogue of Ritter & Kolb (1998) as a starting
point. We find there are 55 reliable spectral type determinations and only 14
reliable mass determinations of CV secondary stars (10 and 5, respectively, in
the case of LMXBs). We derive new spectral type-period, mass-radius,
mass-period and radius-period relations, and compare them with theoretical
predictions. We find that CV secondary stars with orbital periods shorter than
7-8 hours are, as a group, indistinguishable from main sequence stars in
detached binaries. We find it is not valid, however, to estimate the mass from
the spectral type of the secondary star in CVs or LMXBs. We find that LMXB
secondary stars show some evidence for evolution, with secondary stars which
are slightly too large for their mass. We show how the masses and radii of the
secondary stars in CVs can be used to test the validity of the disrupted
magnetic braking model of CV evolution, but we find that the currently
available data are not sufficiently accurate or numerous to allow such an
analysis. As well as considering secondary star masses, we also discuss the
masses of the white dwarfs in CVs, and find mean values of M_1 = 0.69+/-0.13
M_sun below the period gap, and M_1 = 0.80+/-0.22 M_sun above the period gap.
