Abstract We present a marginal stability curve of a deformable bubble ascending freely in a viscous Newtonian liquid. The bubble is considered in the limit of zero gas/liquid density and viscosity ratio as an incompressible void of deformable shape. The marginal stability curve is given in the two-parameter plane of the Galileo number G a = g d 3 / ν and of the Bond number B o = ρ g d 2 / σ where g denotes the gravitational acceleration, d the diameter of the undeformed spherical bubble and ν, ρ and σ are, respectively, the kinematic viscosity, the density and surface tension of the liquid. The numerical investigation covers more than two decades of Bond number going from 0.1 to 20. The results clearly show the crucial role of the surface deformation in the loss of stability of the steady axisymmetric flow.