Extending the previous work done by the authors, this paper develops a time domain synthesis method for the classical guitar based on substructuring concepts and using the Udwadia-Kalaba modeling strategy. Adopting a modal description of the dynamics of the separate flexible subsystems in terms of their unconstrained modes and enforcing coupling constraint conditions for the assembly, the result is an explicit dynamical modal formulation for the coupled system that directly lends itself to time-stepping methods for simulation. The guitar model couples six strings through an experimentally based body model of an actual instrument, includes two string polarizations, and the string geometrical nonlinear effects, as well as the string/fret interaction as the instrument is played. Details are given for putting all the vibrating components together in a satisfying manner, and a specific strategy is explored to allow for a nonrigid fret using flexible-dissipative-inertial constraints. The reliability of the approach is demonstrated with simulation examples that confirm the features one would expect regarding the dynamical behavior of classical guitars. Finally, a pragmatic approach is made to calculate the radiated sound by convolution, combining the computed bridge force with a measured vibro-acoustic impulse response of the instrument, which proved to give satisfactory sounding results.