An attempt is made to calculate pressure drops in, the, laminar and the turbulent flow of generalised, purely-viscous, non-Newtonian liquids in curved conducts of elliptic. cross-section. Second variant of the several-stage transformation method is proposed. New dimensionless equations describing both the non-Newtonian flow and its pseudo-Newtonian analogue have been found. The experimental data obtained by the author shows good agreement with theory.