Results from experiments conducted in downward liquid-gas flows in inclined, eccentric annular pipes, with water-air and water-polymer-air mixtures as the working fluids, are presented. The gas was injected near the middle of the test-section length. This flow is directly relevant to what is found in down-grade portions or "horizontal" wells. Flow maps, in terms of liquid and gas superficial velocities, indicating the transitions between counter-current and co-current gas flows have been determined experimentally for four dip angles. The counter-current gas flow observed was always in the slug regime while the co-current one appeared as stratified. Counter-current flow fraction and void fraction measurements were carried out at various liquid superficial velocities and gas-injection rates and correlated to visual observations through a full-scale transparent test section. Results indicate that increase of the liquid yield point favors the development of counter current flow which is shown to occur at representative liquid superficial velocities and gas injection rates. Thus, counter-current flow can be easily generated at small downward dip angles, within the practical range of liquid superficial velocity for drilling operations, especially at low gas-injection rates.