  Square lattice Heisenberg and XY antiferromagnets with uniaxial anisotropy in
a field along the easy axis are studied. Based on ground state considerations
and Monte Carlo simulations, the role of biconical structures in the transition
region between the antiferromagnetic and spin--flop phases is analyzed. In
particular, adding a single--ion anisotropy to the XXZ antiferromagnet, one
observes, depending on the sign of that anisotropy, either an intervening
biconical phase or a direct transition of first order separating the two
phases. In case of the anisotropic XY model, the degeneracy of the ground
state, at a critical field, in antiferromagnetic, spin--flop, and bidirectional
structures seems to result, as in the case of the XXZ model, in a narrow
disordered phase between the antiferromagnetic and spin--flop phases, dominated
by bidirectional fluctuations.
