A handful of nuclear reactions have been identified as vital for our understanding of explosive stellar phenomena and the nucleosynthesis associated with these scenarios. The 22Ne(α, γ)26Mg reaction in massive stars is responsible for using the neon fuel required for the 22Ne(α, n) 25 Mg, which is a key source of neutrons in these environments. Cl(p, γ) 35 Ar reaction affects the final abundance of 34 S which could be used as an identifier of nova origin of presolar grains. The rate of these reactions is predicted to be dominated by a number of resonant states above the α- and proton-emission thresholds, respectively. Consequently, by determining the nuclear properties of such resonant states it is possible to estimate the 22 Ne(α, γ) 26 Mg and 34Cl(p, γ)35Arreaction rates. In this thesis work, the 11B(16O,p)26Mg and 9Be(28Si,2n)35Ar fusion-evaporation reactions were used to populate excited states in the 26Mg and 35Ar nuclei, respectively. The beams of 16O and 28Si were produced by the Argonne Tandem Linear Accelerator System and prompt electromagnetic radiation was detected using the GAMMASPHERE detector array, which, in the case of the 35Ar experiment, was used in coincidence with recoil selection provided by the Argonne Fragment Mass Analyzer. The two γ-ray spectroscopy studies performed in this work allowed a determination of the nuclear properties of astrophysically important γ-decaying states, which, in turn, were used to re-evaluate the 22 Ne(α, γ)26Mg and 34Cl(p,γ)35Ar stellar reaction rates.