This invention describes novel hydrophobically associating terpolymers containing sulfonate functionality which are useful as aqueous fluid rheology or flow modifiers. These high molecular weight water soluble polymers contain both water soluble and water insoluble monomers. The water soluble monomers are acrylamide (AM) and a salt of an ethylenically unsaturated sulfonic acid (S) and the water insoluble monomer is a higher alkyl acrylamide (R). These polymers are referred referred to as SRAM. The process for their preparation relies on solubilizing the water insoluble monomer into an aqueous micellar solution containing one or more surfactants and the water soluble monomers. The surfactants are specifically selected to enable homogeneous dispersion of the hydrophobic monomer(s) in the presence of anionic sulfonate containing monomers. Redox or free radical initiators are used to copolymerize both the water soluble and water insoluble monomers, forming terpolymers of ethylenically unsaturated sulfonic acids, alkylacrylamides and acrylamide. Aqueous solutions of these hydrophobically associating polymers exhibit enhanced viscosification, reduced salt sensitivity and other desirable rheological properties found useful in a variety of applications.