  BaCuSi$_2$O$_6$, a $S=1/2$ quantum antiferromagnet with a double-layer
structure of Cu$^{2+}$ ions in a distorted planar-rectangular coordination and
with a dimerized spin singlet ground state, is studied by means of the electron
paramagnetic resonance technique. It is argued that multiple absorptions
observed at low temperatures are intimately related to a thermally-activated
spin-triplet exciton superstructure. Analysis of the angular dependence of
exciton modes in BaCuSi$_2$O$_6$ allows us to accurately estimate anisotropy
parameters. In addition, the temperature dependence of EPR intensity and
linewidth is discussed.
