The present invention relates to an improved continuous phase for an oil based drilling fluid and specifically a synthetic hydrocarbon continuous phase which is non-polluting and minimally toxic. The invention provides excellent drilling fluid properties under a wide variety of drilling conditions. The synthetic hydrocarbons are selected from the group consisting of branched chain oligomers synthesized from one or more olefins containing a C.sub.2 to C.sub.14 chain length and wherein the oligomers have an average molecular weight of from 120 to 1000. In the drilling fluid compositions, suitable emulsifiers, wetting agents, viscosifiers, weight materials and fluid loss additives are utilized in conjunction with water and/or a brine phase for the desired rheological properties.