A systematic analysis is made of the possible free energy diagrams for a binary titanium alloy consisting of a metastable beta phase, which tends to form either the alpha or the omega phase, or both. The predictions based on each of the possible free energy diagram configurations are compared with the available experimental data. Arguments are developed to show that it should be possible to nucleate an omega phase having an initial solute content less than the metastable equilibrium value and not necessarily a higher solute concentration, as suggested by other investigators. It is further shown that the observed precipitation of a solute-lean beta phase in certain binary and ternary beta alloys cannot be explained in terms of an ordinary miscibility gap resulting from a preference for bonds between like atoms rather than bonds between unlike atoms. An explanation is suggested on the basis of an early model proposed by M. K. McQuillan in which the electronic structure of the titanium atom can change with temperature leading to two possible types of bonding behaviour.