While the oxidative stability of single walled carbon nanotubes has been studied extensively, very little is known about the diameter dependence of oxidative stability in multiwalled carbon nanotubes (MWNTs) and the effect of vacuum annealing on such stability. We have investigated six sets of samples with different diameters in the range of 5–100 nm systematically by thermogravimetric analysis (TGA) before and after vacuum annealing. High resolution transmission electron microscopy studies provide evidence for structural defects in the nanotube walls. Further, it reveals that with increasing diameter, interlayer d-spacing between concentric tubes decreases. Experimental TGA profile is found to constitute multiple components of oxidation as revealed from reverse Sigmoidal fitting. Analysis of the TGA profile shows that the oxidation temperature follows an exponential recovery function with increasing diameter, while width of the differentiated TGA spectra decreases. It is shown that oxidative stability of lower diameter MWNTs are primarily controlled by lattice strain, while that of large diameter MWNTs is decided by the defects in the nanotube wall. High vacuum annealing studies in the temperature range 300–1000 °C show major improvement in the structure and oxidative stability for MWNTs annealed at 500 °C. Results are compared with those of the single walled nanotubes. The observed diameter dependence is explained on the basis of strain in the nanotube lattice and defects in the nanotube walls.