The linear stability of paraboloidal dendrites is analyzed by perturbing its shape. We consider two types of perturbation modes: tip splitting and branch formation. The operating point for the dendrite is evaluated by using a marginal stability hypothesis for its tip. In particular, the stability constant for dendrites growing with cubic symmetry is found to be sigma* = 0.0156, when the thermal diffusion in the solid phase is allowed. The predictions of our model are in very good agreement with reliable experimental results for water and succinonitrile, and with the fact that, although the marginal stability does not represent the correct physics of the tip selection process, represents a very useful criterion in general experimental conditions. (C) 2002 International Association for Hydrogen Energy. Published by Elsevier Science Ltd. All rights reserved.