This paper presents a theoretical model to predict film condensation heat transfer in square section horizontal microchannels. The model is based on fundamental analysIS ssuming laminar condensate flow on the channel walls taking account of surface tension, vapour shear stress and gravity. Sample numerical results are given for R134a, and channel size (side of square) 1.0 mm. The general behaviour of the condensate flow pattern (spanwise and streamwise profiles of the condensate film), as well as streamwise variation in quality and local mean (over section perimeter) heat-transfer coefficient, are qualitatively in accord with expectations on physical grounds.