This study looks at the dynamics of a particle suspended in a viscoplastic fluid, flowing in a horizontal circular cylindrical pipe. Inertia effects are negligible in comparison with viscous effects and plastic effects. The suspensions are highly stabilized and at rest the spheres cannot settle under gravity alone. The results of Merkak et al. (AIChE J. 2008;54:1129-1138) are extended, taking into consideration both particles of the same density or denser than the fluid and pipe-to-particle diameter ratios of 8 or 56. New migration phenomena in the sheared zone are thus evidenced when buoyancy forces are nil. It? the case of particles denser than the fluid, it is shown how the spheres settle by bypassing the plug-flow zone. A map showing the stability of flowing suspensions could, thus, be drawn. (C) 2009 American Institute of Chemical Engineers AIChE J, 55: 2515-2525, 2009