A method of drilling a gas or oil well consists of use of a water-based drilling fluids containing high molecular weight crosslinked polyacrylic acid as viscosifying agent. The drilling fluid may further contain a lubricant, weighting agent and/or a wetting agent as well as a synthetic silicate or smectite clay. The aqueous based drilling fluid exhibits a coefficient of friction which is substantially close to the coefficient of friction of oil based drilling muds. The drilling fluid exhibits stability at well temperatures in excess of 150° C.