Evaporating heat transfer coefficients of R-22 and R-134a were measured in smooth horizontal copper tubes with inner diameters of 1.77, 3.36 and 5.35mm, respectively. The experiments were conducted in a closed loop, which was driven by a magnetic gear pump. Experiments were performed for the following range of variables: mass velocity (200 to 400 kg/$m^2$.s), saturation temperature($0^{circ}C,; 5^{circ}C$) and quality(0 to 1.0). Main results obtained are as follows: evaporating heat transfer coefficients in the small diameter tubes (ID<7mm) were observed to be strongly affected by various diameters and to differ from those in the large diameter tubers. The heat transfer coefficients of the small diameter tubes were higher than those of the large diameter tubs. And it was very difficult to apply some well-known previous predictions (Shah`s, Gungor-Winterton`s and Kandlikar`s correlation) to small diameter tubes.