  It was recently demonstrated that contact binaries occur in globular clusters
(GCs) only immediately below turn-off point and in the region of blue straggler
stars (BSs). In addition, observations indicate that at least a significant
fraction of BSs in these clusters was formed by the binary mass-transfer
mechanism. The aim of our present investigation is to obtain and analyze a set
of evolutionary models of cool, close detached binaries with a low metal
abundance, which are characteristic of GC. We computed the evolution of 975
models of initially detached, cool close binaries with different initial
parameters. The models include mass exchange between components as well as mass
and angular momentum loss due to the magnetized winds for very low-metallicity
binaries with Z = 0.001. The models are interpreted in the context of existing
data on contact binary and blue straggler members of GCs. The model parameters
agree well with the observed positions of the GC contact binaries in the
Hertzsprung-Russell diagram. Contact binaries in the lower part of the cluster
main sequence are absent because there are no binaries with initial orbital
periods shorter than 1.5 d. Contact binaries end their evolution as mergers
that appear in the BS region. Binary-formed BSs populate the whole observed BS
region in a GC, but a gap is visible between low-mass mergers that are
concentrated along the zero-age main sequence and binary BSs occupying the red
part of the BS region. Very few binary mergers are expected to rotate rapidly
and/or possess chemical peculiarities resulting from the exposure of the layers
processed by CNO nuclear reactions. All other binary mergers are
indistinguishable from the collisionally formed mergers. The results show that
binary-formed BSs may constitute at least a substantial fraction of all BSs in
a GC.
