Lineage specification of hematopoietic stem cells is considered a progressive restriction in lineage potential. This view is consistent with observations that differentiation and lineage specification is preceded by a low-level coexpression of lineage specific, potentially antagonistic genes in early progenitor cells. This coexistence, commonly referred to as priming, disappears in the course of differentiation when certain lineage-restricted genes are upregulated while others are downregulated. Based on this phenomenological description, we propose a quantitative model that describes lineage specification as a competition process between different interacting lineage propensities. The competition is governed by environmental stimuli promoting a drift from a multipotent coexpression to the dominance of one lineage. The assumption of a context-dependent intracellular differentiation control is consistently embedded into our previously proposed model of hematopoietic stem cell organization. The extended model, which comprises self-renewal and lineage specification, is verified using available data on the lineage specification potential of primary hematopoietic stem cells and on the differentiation kinetics of the FDCP-mix cell line. The model provides a number of experimentally testable predictions. From our results, we conclude that lineage specification is best described as a flexible and temporally extended process in which lineage commitment emerges as the result of a sequence of small decision steps. The proposed model provides a novel systems biological view on the functioning of lineage specification in adult tissue stem cells and its connections to the self-renewal properties of these cells.