The simplified quasi-one-dimensional model of thermoacoustic devices formulated in Part I [Watanabe et al., J. Acoust. Soc. Am.102, 3484–3496 (1997)] is studied in the nonlinear regime. A suitable numerical method is described which is able to deal with the steep waveforms that develop in the system without inducing spurious oscillations, appreciable numerical damping, or numerical diffusion. The results are compared with some experimental ones available in the literature. Several of the observed phenomena are reproduced by the model. Quantitative agreement is also reasonable when allowance is made for likely temperature nonuniformities across the heat exchangers.