An asymptotic analysis is utilized in the solution procedure of the spray governing equations in order to examine droplet coalescence effects on spray diffusion flames in a unidirectional shear layer flow. The spray diffusion flame results from an evaporating multisize (polydisperse) spray of fuel droplets suspended in one of the streams of the unidirectional shear layer flow. The droplets and their vapor spread into a co-flowing stream in which the oxidizer is contained and feed the flame. Simultaneous concurrent processes of evaporation and coalescence of fuel droplets are considered. A small parameter defined in terms of a characteristic coalescence rate is identified in the governing equations and then employed in the asymptotic solutions. Various values of this parameter are analyzed. The lateral location of the flame and its temperature are obtained here via the solution of Schvab-Zeldovich-type equations. New results are presented for the effects of droplet coalescence on the evolution in drop size histograms, on droplet Sauter mean diameter (SMD), on vapor production across the shear layer, and on flame geometry and its temperature. The present results indicate that for relatively high coalescence rates, the lateral distributions of the droplet SMD across the shear layer assumes an S-shaped curve. It is also shown that sprays that are initially comprised of small droplets produce larger amounts of vapor and thus result in a flame that is shifted toward the oxidizer stream. On the other hand, larger droplets are formed at the expense of small droplets via coalescence. Thus, due to droplet coalescence, the resulting flame is shifted toward the fuel spray stream. The higher the coalescence rate, the smaller is the vapor production rate and the more pronounced is the shift of the flame toward the fuel spray stream. Various initial drop size histograms are considered here. The results of the present study indicate that flame location and its temperature are functions not only of the total flow rate of liquid fuel but also of the initial drip size histogram of the spray and may be affected by droplet coalescence.