We have studied the magnetic properties of MnAs epilayers grown in two preferred orientations on (001) GaAs by molecular-beam epitaxy. Samples with the ((1) over bar 100) MnAs parallel to (001) GaAs ("type A") show asymmetric hysteresis loops and an anomalous temperature dependence of the coercive field. We attribute these anomalies to intrinsic exchange biasing effects arising from the presence of a strain-induced antiferromagnetic beta -MnAs phase that coexists with the ferromagnetic alpha -MnAs phase. These unusual effects vanish with decreasing sample thickness, suggesting a strategy for suppressing the antiferromagnetic beta -MnAs phase. (C) 2001 American Institute of Physics.