The competition of different kinds of orderings near the spinflop bicritical point of antiferromagnets gives rise to a new type of critical behavior governed by the anisotropy crossover exponents. We have measured the magnetic phase diagram of MnF2 in the vicinity of the spinflop bicritical point using susceptibility and NMR. For a carefully aligned sample (misalignement of the applied field with respect to the easy axis of magnetization <2×10−6 rad) we obtained for the crossover exponent φ=1.26±0.03, in good agreement with theory. The experiment further yields the orientation of the field scaling axis and the universal critical line amplitude ratio Q both in only fair agreement with theory.