We present experimental results bearing on the random-field problem near the bicritical point (BCP) of antiferromagnetic GdAlO3 with various degrees of dilution: 1) From the phase boundaries near the BCP, a random-field crossover exponent φrf≊1.75 is derived. 2) At random-exchange transitions, the susceptibility χ̄ exhibits a divergence-like peak as in the pure material. At random-field transitions, on the other hand, only a broad maximum of χ̄ is observed, suggesting a specific-heat exponent α<-1. 3) The transition from the antiferromagnetic state to the spinflop state below the bicritical point is qualitatively different from the pure case. 4) In the paramagnetic state above the bicritical point, an additional susceptibility peak is observed, whose intensity increases rapidly with the degree of dilution. These results are compared with current theory on the random-field problem.