Rapid decompression experiments were performed to study homogeneous bubble nucleation in a crystal-free rhyolitic liquid at 800¿C. Bubble nucleation was produced by lowering the pressure at 1--10 MPa s-1 from an initial value between 200 and 295 MPa to a final value below the volatile saturation pressure PSat. Six volatile compositions with 4.1--7.7 wt % H2O and 10--1200 ppm CO2 were investigated. For each composition we determined the critical pressure PHoN below which homogeneous nucleation can proceed. The samples quenched below PHoN showed a nucleated core with a large number of uniformly spaced bubbles. With decreasing pressure, bubble number densities increased from 1015 m-3. The degree of supersaturation required for homogeneous nucleation, ΔPHoN (= PSat - PHoN), increased with decreasing H2O content or increasing CO2 content. Huge values of ΔPHoN, ≥135 to 310 MPa, were measured in the H2O-poor compositions (4.1--4.6 wt % H2O; 50--1100 ppm CO2); much lower values from ≈60 to 160 MPa were obtained in the H2O-rich compositions (7.0--7.7 wt % H2O; 10--630 ppm CO2). The high ΔPHoN in liquids with 4--5 wt % H2O should result in the buildup of large degrees of supersaturation during magma ascent, a very late nucleation event, and a rapid (explosive) vesiculation. By contrast, rhyolitic liquids with much larger water contents have higher saturation pressures and much lower ΔPHoN: bubble nucleation may therefore occur at depth in the volcanic conduit favoring a subsequent near-equilibrium degassing.