This paper contains a statistical analysis of the dose-time factors influencing late complications in 784 patients with squamous cell carcinomas of the pharynx or larynx treated with external beam irradiation only at the University of Florida. The patients include 560 who received continuous course once-a-day therapy, 116 who received twice-a-day treatment, and 108 who received a once-a-day split course regimen. Both 2+ and 3+ complications were considered. Fifty-six patients developed either of these complications. The factors included in the analysis were site and size of the primary, total dose, fraction size, and treatment time. The linear-quadratic model was used to incorporate fraction size into the analysis. Proportional hazards analysis, which models the time to occurrence of the late complication, was used to quantify the joint influence of the above patient and fractionation variables on the incidence of late effects. The occurrence of the late effects was heterogeneous, with only a weak relationship to the patient and fractionation variables. The influence of the size of the primary was significant, with larger primaries associated with higher complication rates independent of fractionation variables. For oropharynx primary sites there was no significant effect of the fractionation variables. For larynx and hypopharynx, excluding T1-T2 true vocal cord, there was a significant effect of total dose and fraction size. The alpha/beta ratio was estimated to be 7.8 Gy (95% confidence interval, 3.0, infinity). There was no significant effect of overall treatment time. The estimated 2+ complication rate at 1 year from 68 Gy given in 2 Gy fractions in 50 days is 0.1% for T 1-2 vocal cord, 4.1% for T1-T2 supraglottic larynx, 3.8% for T3 supraglottic larynx and vocal cord, 14.9% for T4 supraglottic larynx, 6.7% for T1-T2 tonsil and soft palate, 7.6% for T3-T4 tonsil and soft palate, 7.0% for T1-T2 pyriform sinus and pharyngeal wall, and 13.0% for T3-T4 pyriform sinus and pharyngeal wall.