  Using Monte Carlo simulations, we study the critical behavior of two models
of frustrated XY antiferromagnets with a collinear spin ordering and with an
additional twofold degeneracy of the ground state. We consider a classic
antiferromagnet on a body-centered cubic lattice with an additional
antiferromagnetic exchange interaction between next-nearest spins, and a
ferromagnet with an extra antiferromagnetic intralayer exchange. In both
models, a single first-order transition on the discrete and continuous order
parameters is found. Observed critical pseudo-exponents are in agreement with
exponents of XY magnets with a planar spin ordering like a stacked-triangular
antiferromagnet and helimagnets belonging to the same symmetry class.
