This paper investigates the steady flow and heat transfer between two concentric spheres with the inner rotating and the outer one stationary for the gap width of sigma=0.18. A continuation method is applied to study the bifurcation structure of the discretized governing equations. The resulting Jacobian matrix along with a test function approach is used to locate the bifurcation points. A bifurcation diagram of the flow is constructed for Re < 1200. Seven steady flow modes are predicted. Linear stability analysis is used to determine the stability of each flow mode. Temperature distribution and heat transfer rate of each flow mode are also computed and analyzed. (C) 2000 Elsevier Science Ltd. All rights reserved.