A two-phase volume-averaging model developed for the simulation of the dynamic decomposition and solidification of hypermonotectic alloys was used to study the occurrence of convection phenomena during directional solidification of a hypermonotectic alloy (Al-10wt.%Bi) under terrestrial condition. The model accounts for nucleation and growth of secondary phase droplets, Marangoni and Stokes forces, solute partitioning, heat release due to decomposition and solidification. It is shown that the appearance and growth of secondary droplets is accompanied with a continuous downwards motion of droplets, which rapidly becomes unstable. After relaxation of this dynamic motion the advancing solidification front freezes in the resulting non-uniform droplet distribution.