The value of marker-assisted selection in dairy cattle breeding schemes is predicted by a deterministic model. In these schemes, associations between markers and milk production were assessed from production records of daughters of a grandsire by a multiple regression model with random marker effects. By tracing markers from the grandsire to grandoffspring, deviations of grandoffspring from their full-sib family mean were predicted. Predictions of the within-family variance of the grandoffspring accounted for by markers amounted to up to 13.3%. This figure decreased when the number of daughters of the grandsire analyzed decreased and, less markedly, when the distance between flanking markers increased. Prediction of within-family deviations hardly improved rates of genetic gain in conventional progeny testing schemes; equal numbers of young bulls were born annually. Genetic gain and improvement of genetic gain because of prediction of within-family deviations were much higher in nucleus schemes. In these schemes, with short optimized generation intervals, conventional selection was mainly for pedigree information and did not use the within-family variance. Analysis of highly polymorphic markers in daughters of both grandsires accounted for 4.1 to 13.3% of the within-family variance, which increased rates of gain by 9.5 to 25.8% and 7.7 to 22.4% in open and closed nucleus schemes, respectively. Risk of breeding schemes, measured by the variance of the selection response, was not increased by the use of markers.