Anticipation, i.e. a decreasing age-at-onset in subsequent generations has been observed in a number of genetically triggered diseases. The impact of anticipation is generally studied in affected parent-child pairs. These analyses are restricted to pairs in which both individuals have been affected and are sensitive to right truncation of the data. We propose a normal random effects model that allows for right-censored observations and includes covariates, and draw statistical inference based on the likelihood function. We applied the model to the hereditary nonpolyposis colorectal cancer (HNPCC)/Lynch syndrome family cohort from the national Danish HNPCC register. Age-at-onset was analyzed in 824 individuals from 2-4 generations in 125 families with proved disease-predisposing mutations. A significant effect from anticipation was identified with a mean of 3 years earlier age-at-onset per generation. The suggested model corrects for incomplete observations and considers families rather than affected pairs and thereby allows for studies of large sample sets, facilitates subgroup analyses and provides generation effect estimates.