In this work we propose an effective viscosity criterion for the stabilization of annular gas-liquid and Liquid-particle flows and an inertial mechanism which drives waves into slugs in slugging gas-liquid hows. Annular Bow is stable when the fluid having the higher effective viscosity occupies the core region and the lower viscosity fluid is in the annulus. The eddy viscosity criterion is shown to be very consistent with published work on annular how transitions in horizontal and vertical gas-liquid Bows. It also applies to a variety of liquid-solid and gas-solid flows. In the second part of the paper we propose a mechanism for explaining the growth of initially small waves and initiation of slugs in gas-liquid how.