The continuous-cooling transformation behaviour of Ti - 45.5 at.% Al-0.05 at.% B alloy was quantitatively measured using a real-time resistivity temperature - time measurement apparatus operating under a high vacuum. The addition of a small amount of B does not significantly alter the alpha - gamma-phase equilibria but significantly raises the alpha - gamma lamellar start temperature of Ti - 45.5 at.% Al alloy at most cooling rates. Furthermore, it markedly increases the critical cooling rate for the ordering reaction. The effect of B addition, which greatly stabilizes the lamellar structure up to a fast cooling rate, is to accelerate the lamellar formation kinetics; the lamellar spacing was nevertheless distinctively larger in a B-doped alloy. This is because lamellae in B-doped alloy nucleate heterogeneously on titanium borides at the grain boundary; the borides are effective nucleation sites particularly since local Ti depletion can occur near the interface of the growing titanium borides during cooling. In the absence of B addition, the lamellar structure starts to form only at temperatures below T-0, suggesting that a large undercooling is required for the nucleation of lamellae even at the grain boundaries. On the other hand, the B addition greatly retards the kinetics of the alpha-to-alpha(2) ordering reaction by markedly increasing its critical cooling rate without a large change in the ordering temperature. This is believed to be due to its tendency to segregate strongly to the antiphase boundaries.