Aliphatic hydrocarbons (and, at some extent, also aromatic hydrocarbons) are very resistant to oxidation under conventional oxidation conditions. However, free radicals (in particular the very reactive and oxidizing hydroxyl radical) can react with saturated hydrocarbons. This occurs by hydrogen abstraction, leading to an alkyl radical, that in oxidizing media can undergo a sequence of reactions yielding aldehydes, ketones or (in an ultimate degree) even CO2. This occurs for instance in wastewater treatment plants and is the principle of the "Advanced Oxidation Processes" (AOP's), where ionizing (beta or gamma) radiation is used to generate oxidizing radicals by water radiolysis.
If you refer to conventional oxidative processes, aliphatic hydrocarbons are generally resistant to oxidation. At special conditions, oxidation resistance is very low. And do not forget microorganisms that have the capacity of degrading the hydrocarbons.
I don't seem to know why all these answers are coming. Is it because of the word refractory? A hydrocarbon that is resistant to oxidation, stubborn to and unmanageable is siad to be refractory to oxidation. The process of oxidation mediated by monooxygenases and dioxygenases is the dominant process involved in hydrocarbon degradation. The fraction most susceptible to degradation (by oxidation) are the n-alkanes (saturates). There are way too many review articles on the biodegradability potentials of hydrocarbon fractions. Please see the attached documents