The authors have recently used a combination of classical elasticity theory and Miedema's model for the heat of formation of alloys to predict the glass-forming ranges of binary transition metal systems. In this paper they extend this approach to study the glass-forming regions in the ternary case. The predictions of the theory are compared with available experimental information for some Co-based ternary alloys, and they relate their treatment to the empirical equation recently proposed by Ueno and Waseda (1985) to describe the minimum solute concentration for glass formation in ternary systems.