Layered transition metal dichalcogenides (TMDs) are being considered as a promising alternative channel material in ultra-thin and low power nanoelectronics, due to the significant tunability of their electronic properties via mechanisms such as mechanical strain, control of the material thickness, application of an external field, impurities, doping, alloying, or altering the substrate nature. Initially, monolayer TMDs as counterparts to graphene captured the attention of the scientific community owing to their semiconductor nature with sizable band gaps. However, certain physical and chemical properties of TMDs, such as their oxygen reactivity and stability in air need to be more completely understood in order to crystallize the promising superior performance of TMD-based electronic devices. Here, a comparative analysis of the stability of various TMDs (MX2: M = Mo, W; X = S, Se) in air is performed using density-functional theory (DFT) as well as x-ray photoelectron spectroscopy (XPS). We find that the surface chemistry of the basal plane of sulfides and selenides is relatively stable in air although for completely different reasons, which can be explained by investigating oxygen dissociative adsorption kinetics and thermodynamics. On the contrary, the edge of MX2 nanoribbons shows strong driving forces towards O2 dissociation and chemisorption. Our combined theoretical and experimental investigation reveals that the air stability of TMDs should not be placed in the same footing that other 2D materials, like graphene. Thus, this work highlights the importance of having controlled oxygen environment during crystal exfoliation/ growth and defect passivation in order to provide high quality uniform materials for TMD-based device fabrication.