The thermal stability in air of solar selective coatings based on the novel MoSi2-Si3N4 hybrid composite has been investigated here for the first time. Although thermal stability of solar absorbers is typically examined under vacuum, high temperature air stability is required for practical applications in concentration solar power (CSP) technologies: solar tower systems receivers operate in air and, on the other hand, air stability is highly preferred in parabolic trough collector systems due to occasionally undesired losses of vacuum conditions. In this work, the effect of different layers combination, prepared by sputtering, on the optical performance after high temperature annealing has been investigated. Two different standard substrates (stainless steel and Inconel) have been explored. It is shown that silver layer, typically used in SSC as IR reflector, strongly affects the stack thermal stability in air, leading to important degradation. For SSC stacks with the Inconel/MoSi2-Si3N4/Si3N4 structure (onto Inconel substrate), a good thermal stability in air is obtained, leading to just a slight variation of the absorptivity after air annealing at 600 degrees C, probably due to partial Si3N4 oxidation. Best optical performance is achieved for the Inconel substrate, using and additional Al2O3 barrier on top, comprising the stack the following structure: Inconel/MoSi2-Si3N4/Si3N4/Al2O3. This combination exhibits very good optical performance, even after annealing at 700 degrees C in air. The Performance Criterion (PC) according to the International Energy Agency, evaluated after successive air annealing cycles of 100 h at 600 degrees C, gets 0.02, which is considerably smaller than 0.05, fulfilling this material the PC for practical applications. Our results evidence that the MoSi2-Si3N4 absorber deposited onto Inconel substrate and capped with a Si3N4/Al2O3 layer on top (acting as antireflective and protective barrier) is a very promising selective coating for solar receivers operating in air at temperatures about 600 degrees C.