Deep Level Transient Spectroscopy (DLTS) has been applied to MOS capacitors (MOSCAPs) fabricated on n- and p-type GaAs and on n-type InxGa1-xAs epitaxial layers deposited by MBE on GaAs substrates. The gate dielectric consists of 10 nm ALD Al2O3. It is shown that the dominant deep levels in the case of GaAs MOSCAPs are two broad interface-state-related bands centered around midgap, which appear to be very similar to what has been found in the past for other gate dielectrics on GaAs. At the same time, it is reported that the interface-state peak shifts closer to the conduction band for the InxGa1-xAs layers, whereby the activation energy becomes smaller for higher x. However, it is demonstrated that in this case not only interface states contribute to the DLTS emission signal but also deep levels associated with threading dislocations (TDs) in the relaxed layers. This contribution grows progressively with the In content, i.e., with the amount of relaxation. From this, it is concluded that InxGa1-xAs/GaAs substrates are not favorable for inversion-type of MOS devices due to the increasing impact of the TDs on the device performance.