The float-zone crystal-growth process is studied in the framework of the half-zone model. Linear-stability analysis is used to compare the onset of oscillations in liquid-bridge thermocapillary convection upon liquid-bridge volume with experimental data for high-Prandtl fluid. Well-known structure of neutral stability curve for high-Prandtl fluid, consisting of two branches separated by an "overstability" gap, has been clearly reproduced. Moreover, for low-volume branch there is a good quantitative correspondence between experimental data and linear-stability analysis. Travelling hydrothermal waves with unit azimuthal wave number correspond to critical perturbations for both branches. In addition, an influence of temperature-dependent viscosity on stability limits is determined. (C) 2004 Elsevier B.V. All rights reserved.