  The spin structure and spin dynamics of excitons in an ensemble of
(In,Al)As/AlAs quantum dots (QDs) with type-I band alignment, containing both
direct and indirect band gap dots, are studied. Time-resolved and spectral
selective techniques are used to distinguish between the direct and indirect
QDs. The exciton fine structure is studied by means of optical alignment and
optical orientation techniques in magnetic fields applied in the Faraday or
Voigt geometries. A drastic difference in emission polarization is found for
the excitons in the direct QDs involving a $\Gamma$-valley electron and the
excitons in the indirect QDs contributed by an $X$-valley electron. We show
that in the direct QDs the exciton spin dynamics is controlled by the
anisotropic exchange splitting, while in the indirect QDs it is determined by
the hyperfine interaction with nuclear field fluctuations. The anisotropic
exchange splitting is determined for the direct QD excitons and compared with
model calculations.
