We examined temporal dependencies between repeated assessments of respiratory tract infections (RTIs) and asthma in children in the Leicester Respiratory Cohort, Leicestershire, United Kingdom. Information associated with asthma (i.e., doctor diagnosis, health care visits, wheeze frequency) and RTIs (i.e., cold duration and frequency, cough with colds, ear infections) in the previous 12 months was assessed repeatedly at ages 1, 4, and 6 years for children born between April 1996 and April 1997. We determined associations between contemporaneous and lagged measures of asthma and RTIs, using structural equation modelling. In 1,995 children, asthma was positively associated with contemporaneous infections. Asthma at age 6 years was positively associated with asthma at age 4 years (regression coefficient = 0.87; 95% confidence interval (CI): 0.76, 0.97), but not with asthma at age 1 year (regression coefficient = -0.01; 95% CI: -0.14, 0.11). We found no evidence for direct protective effect of infections at age 1 year on asthma either at age 4 (regression coefficient = -0.20; 95% CI: -0.51, 0.10) or 6 (regression coefficient = 0.24; 95% CI: -0.04, 0.52) years. Adjusting for potential confounders did not qualitatively change those relationships. Based on our findings, we suggest that asthma at age 6 years is directly influenced by asthma history and only indirectly, if at all, by earlier infection episodes. We found little support for a protective effect of preschool infections on asthma at early school age.