Open nucleus systems (ONS) have been used in sheep breeding for a number of years, usually in group breeding schemes. In the simplest form the population is divided into two tiers, the nucleus flock composed of elite individuals, while the base, which forms the majority of the population, is usually sub-divided into a number of individual flocks. Animals born in the nucleus may be selected as replacements in the base, while superior animals born in the base may become part of the breeding population of the nucleus. The optimum structure and genetic benefits of using an ONS under Australasian conditions have been extensively studied using deterministic predictions (James, 1977; Mueller and James, 1983). However, subsequent advances in genetic evaluation (e.g. the application of Best Linear Unbiased Prediction (BLUP)) and the smaller flock sizes typical in Europe, are likely to impact on the outcome and optimum structure of such systems.