In the present study, the vaporization processes of the carbide materials with the Ti2SiC, Ti3SiC2, Ti2AlC, Ti3AlC2, Zr2AlC, Zr3AlC2 chemical compositions containing the MAX-phases as well as the oxycarbide systems based on these materials with the addition of hafnia were examined by the Knudsen effusion mass spectrometric method up to the temperature 2200 K. It was established that the main vapor species over the samples with the Ti2AlC, Ti3AlC2, Zr2AlC, and Zr3AlC2 compositions at the temperature 1500 K was atomic aluminum. The samples containing silicon were less volatile compared to the carbide materials with aluminum and transferred into vapor at temperatures exceeding 1900 K to form gaseous Si, Si2, SiC2, and Si2C. The addition of hafnia to the carbides under study led to the formation of oxygen-containing vapor species, particularly Al2O and SiO, and to decrease in the total vapor pressure over the systems formed. It was shown that the samples of the oxycarbide Ti2SiC-HfO2 system were the least volatile materials, and, among the oxycarbide systems containing aluminum, the lowest volatility was observed for the samples of the Zr2AlC-HfO2 system in the case of the hafnia content up to 10 mol. % and of the Ti2AlC-HfO2 system for the higher HfO2 concentration.