Nonlinear viscous droplet oscillations are analysed by solving the Nav
ier-Stokes equation for an incompressible fluid. The method is based o
n mode expansions with modified solutions of the corresponding linear
problem. A system of ordinary differential equations, including all no
nlinear and viscous terms, is obtained by an extended application of t
he variational principle of Gauss to the underlying hydrodynamic equat
ions. Results presented are in a very good agreement with experimental
data up to oscillation amplitudes of 80% of the unperturbed droplet r
adius. Large-amplitude oscillations are also in a good agreement with
the predictions of Lundgren & Mansour (boundary integral method) and B
asaran (Galerkin-finite element method). The results show that viscosi
ty has a large effect on mode coupling phenomena and that, in contradi
ction to the linear approach, the resonant mode interactions remain fo
r asymptotically diminishing amplitudes of the fundamental mode.