We describe simple mathematical models o f gene expression to explore the possible origins o f haploinsufficiency (HI). In a diploid organism, each gene exists in two copies and when one o f these is mutated, the amount o f proteins synthesized is reduced and may fall below a threshold level for the onset o f some desired activity. This can give rise to HI, a manifestation o f which is in the form o f a disease. We discuss both deterministic and stochastic models o f gene expression and suggest possible scenarios for the occurrence o f H I in the two cases. In the stochastic case, random fluctuations around the mean protein level give rise to a finite probability that the protein level falls below a threshold. Increased gene copy number and faster gene expression kinetics reduce the variance around the mean protein level. The difference between slow and fast gene expression kinetics, as regards response to a signal= ing gradient, is further pointed out.