Drilling fluid compositions of the invert oil-based type incorporate (i) as the agent for emulsifying the brine phase in the oil phase, a block or graft copolymer of the general formula (A-COO).sub.m B, where A and B represent polymeric components derived from a specified type of oil-soluble complex monocarboxylic acid and from a water-soluble polyalkylene glycol or polyether polyol, respectively, and m is an integer at least 2, and (ii) as the agent for dispersing solid particulate matter in the oil phase a surfactant containing a C.sub.30-500 hydrocarbon chain as hydrophobic component, and a polar component adsorbable on to the particulate solid surface.