The AramcoMech 3.0 mechanism containing 581 species and 3037 reactions for oxidation of hydrocarbon and oxygenated C0C4 fuels is reduced using six direct relation graph (DRG) related methods for the following fourteen fuels: hydrogen, carbon monoxide, methane, formaldehyde, methanol, acetylene, ethylene, ethane, acetaldehyde, ethanol, propene, 1,3-butadiene, isobutene and 2-butene. Maximum error on ignition delay times increases sharply when certain species is removed from skeletal mechanisms in skeletal reduction and it is difficult to achieve compact skeletal mechanisms for some fuels. This indicates that some important species are identified as redundant species with these methods. A fixed species scheme (FS) is proposed in skeletal reduction, where these species are regarded as important species and are retained in the skeletal mechanism. Smaller skeletal mechanisms can be achieved with this FS method given a certain maximum error. Skeletal mechanisms for each of the fourteen fuels with a maximum ignition delay time error of less than 10% are obtained. A comprehensive skeletal mechanism including 149 species and 925 reactions with a maximum error of 15% on ignition delay times is further achieved using the sensitivity analysis method starting from the union of the skeletal mechanisms for the fourteen fuels. The 149-species comprehensive skeletal mechanism and fourteen skeletal mechanisms are shown to provide reasonably key combustion characteristics for single-component fuels, including the laminar flame speeds, ignition delay times, and major species mole fraction profiles under a wide range of pressures, temperatures and equivalence ratios compared with experimental data and those of the detailed mechanism. Moreover, the 149-species skeletal mechanism can reproduce the combustion properties of some multi-component mixed fuels. The comprehensive skeletal mechanism can be employed as a core reaction base for developing mechanisms of other large hydrocarbon and oxygenated fuels.