Absolutely! Doesn’t get covered very often, but the reaction of C-H bonds with molecular oxygen to give C-OOH primarily occurs with tertiary C-H bonds, C-H bonds adjacent to oxygen (e.g. ethers) and benzylic and allylic C-H bonds.

This is why saturated fats (e.g. margarine) are much less likely to spoil when left out in air than unsaturated fats (e.g. butter)…

Could autooxidation also be considered a reaction of alkanes? I recently came across a problem in my textbook in which methylcyclohexane was converted to methylcyclohexene via auto-oxidation followed by reduction and treatment with an acid.