A preliminary series of quantitative genetic models was applied to a subset of longitudinal height data, spanning birth to maturity, gathered from twin families in the Louisville Twin Study. Descriptive Cholesky factor parameterization was found to give more satisfactory results than did a system of constraints based on a model of developmental transmission of a time-constant and time-specific factors. The results from application of two autosomal sex-limitation models are contrasted with those from a model specifying both autosomal and sex-chromosomal patterns of inheritance. The latter model was more conducive to parameter reduction. Although these models do not constitute conclusive tests of autosomal sex-limitation versus sex-linkage, the more parsimonious model is consistent with previous research suggesting a stature locus on the long arm of the Y chromosome. Heritability of height is estimated at about 90% or greater from 6 years of age on. Substantial and fairly constant longitudinal genetic correlations are found from 3 years of age on. Shared environmental effects unrelated to parental height were seen for birth length, corrected for gestational age, to height at 3 years of age, but these are not satisfactorily differentiated from possible twin effects in the present sample. The genetic consequences of assortative mating are emphasized since failure to take assortment into account can lead to overestimation of shared environmental effects and under-estimation of genetic effects. The results indicate that about 20% of within-gender variability for mature height can be attributed to the genetic consequences of assortment, even though the phenotypic marital correlation of 0.22 is quite modest. The importance of testing the assumption of multivariate normality underlying the application of the method of maximum-likelihood is also highlighted.