We have investigated model systems of silver clusters with different sizes (3 and 15 atoms) deposited on alumina and titania supports using ambient pressure X-ray photoelectron spectroscopy. The electronic structures of silver clusters and support materials are studied upon exposure to various atmospheres (ultrahigh vacuum, O2 and CO) at different temperatures. Compared to bulk silver, the binding energies of silver clusters are about 0.55 eV higher on TiO2 and 0.95 eV higher on Al2O3 due to the final state effect and the interaction with supports. No clear size effect of the silver XPS peak is observed on different silver clusters among these samples. Silver clusters on titania show better stability against sintering. Al 2p and Ti 2p core level peak positions of the alumina and titania support surfaces change upon exposure to oxygen while the Ag 3d core level position remains unchanged. We discuss the origin of these core level shifts and their implications for catalytic properties of Ag clusters.