We study the phase diagram and critical behaviour of the two-dimensional square-lattice fully frustratedXY model (FFXY) and of two related models, a lattice discretization of the Landau–Ginzburg–WilsonHamiltonian for the critical modes of the FFXY model, and a coupled IsingXY model.We present a finite-size-scaling analysis of the results of high-precision Monte Carlo simulations onL × L squarelattices, up to L = O (103).In the FFXY model and in the other models, when the transitions are continuous, there aretwo very close but separate transitions. There is an Ising chiral transition characterized bythe onset of chiral long-range order while spins remain paramagnetic. Then, as temperaturedecreases, the systems undergo a Kosterlitz–Thouless spin transition to a phase withquasi-long-range order.The FFXY model and the other models, in a rather large parameter region, show acrossover behaviour at the chiral and spin transitions that is universal to some extent. Weconjecture that this universal behaviour is due to a multicritical point. The numerical datasuggest that the relevant multicritical point is a zero-temperature transition. A possiblecandidate is the O(4) point that controls the low-temperature behaviour of the 4-vectormodel.