The transition from annular to wavy-stratified oil-water adiabatic flow within horizontal pipes is experimentally analysed and a semi-empirical model is proposed. The transition is referred to as critical because it occurs suddenly, giving rise to a sharp and strong increase in the pressure drop due to the contact of the high-viscosity oil with the pipe wall. This could lead to a dangerous accident in pipelines. Experimental runs were performed on eight test sections of both Plexiglas® and Pyrex® pipes with internal diameters ranging from 21.5 mm to 50 mm, using tap water and oil with viscosity about 880 times higher than that of water. On the basis of pressure drop measurement and flow pattern visualization, the transition boundary between annular and wavy-stratified flow was analytically determined and compared with flow pattern maps.