Discussion of the origin of paramagnetic centres observed by electron paramagnetic resonance in graphene oxide (GO) and reduced graphene oxide (rGO) is done on the assumption that GO can be considered as a functionalized graphene. This leads to the conclusion that the narrow signal with g close to 2, observed for GO and thermally reduced GO, is due to paramagnetic centres localized on defects and exchange coupled to conduction electrons. Randomness of graphene modication results in variety of parameters of EPR signals. The broad signals observed in GO and rGO and ascribed to magnetic clusters on the zig-zag edge states indicate that the edge magnetism can be preserved by functionalization.