  We discuss theoretically phase transitions in frustrated antiferromagnets
with biaxial anisotropy or dipolar forces in magnetic field applied along the
easy axis at $T=0$. There are well-known sequences of phase transitions upon
the field increasing: the conventional spin-flop transition and the flop of the
spiral plane at strong and weak easy-axis anisotropy, respectively. We argue
that much less studied scenarios can appear at moderate anisotropy in which the
magnetic field induces transitions of the first order from the collinear state
to phases with spiral orderings. Critical fields of these transitions are
derived in the mean-field approximation and the necessary conditions are found
for the realization of these scenarios. We show that one of the considered
sequences of phase transitions was found in multiferroic MnWO$_4$ both
experimentally and numerically (in a relevant model) and our theory reproduces
quantitatively the numerical findings.
