Conditions for which the density function of a mixture of two normal distributions is bimodal are investigated. For fixed values of the variances σ12and σ22of the normal distributions if the difference between the means is sufficiently small, the distribution of the mixture will be unimodal, independent of the proportionspand 1 –p, 0 <p< 1. If the difference exceeds a critical value which depends on σ12and σ22the bimodality property then depends onp. Values ofpsufficiently close to zero and one always exist for which the distribution is unimodal.