We examine a competition between the whistler and Alfv¿n fire hoses driven by bi-Maxwellian protons with Tp∥>Tp⊥, where Tp∥ and Tp⊥ are proton temperatures, parallel and perpendicular to the background magnetic field, respectively. We extend the work of Hellinger and Matsumoto [2000> using a two-dimensional hybrid simulation that includes both the instabilities. In the simulation the whistler fire hose initially dominates and saturates in a quasi-linear manner. The Alfv¿n fire hose is not strongly affected by the presence of the whistler fire hose and grows even when the former is saturated. However, as the Alfv¿n fire hose grows and saturates via a conversion to Alfv¿n waves that heat the protons, the waves driven by the whistler fire hose get strongly damped and disappear. The Alfv¿n waves damp as well, so that at the end of the simulation the wave activity is low. The strong decay of the generated waves translates to an important decrease of the proton temperature anisotropy. ¿ 2001 American Geophysical Union