We study the effect that electron-electron interaction has on the prop
erties of a multilayer electron system. We consider the case correspon
ding to filling factor unity in each layer and find that, as a functio
n of the sample parameters, the system has ferromagnetic, canted antif
erromagnetic, or paramagnetic interlayer spin correlations. These thre
e ground states are QHE phases because of the existence of a finite ac
tivation energy. In the ferromagnetic phase the gap is due to the intr
awell exchange energy, whereas in the paramagnetic phase the gap appea
rs due to spatial modulation of the interwell coherence. [S0031-9007(9
8)07800-4].