The present paper describes several models of the central respiratory pattern generator (CRPG) developed employing experimental data and current hypotheses for respiratory rhythmogenesis. Each CRPG model includes a network of respiratory neuron types (e.g., early inspiratory; ramp inspiratory; late inspiratory; decrementing expiratory; postinspiratory; stage II expiratory; stage II constant firing expiratory; preinspiratory) and simplified models of lung and pulmonary stretch receptors (PSR), which provide feedback to the respiratory network. The used models of single respiratory neurons were developed in the Hodgkin-Huxley style as described in the previous paper. The mechanism for termination of inspiration (the inspiratory off-switch) in all models operates via late-I neuron, which is considered to be the inspiratory off-switching neuron. Several two- and three-phase CRPG models have been developed using different accepted hypotheses of the mechanism for termination of expiration. The key elements in the two-phase models are the early-I and dec-E neurons. The expiratory off-switch mechanism in these models is based on the mutual inhibitory connections between early-I and dec-E and adaptive properties of the dec-E neuron. The difference between the two-phase models concerns the mechanism for ramp firing patterns of E2 neurons resulting either from the intrinsic neuronal properties of the E2 neuron or from disinhibition from the adapting dec-E neuron. The key element of the three-phase models is the pre-I neuron, which acts as the expiratory off-switching neuron. The three-phase models differ by the mechanisms used for termination of expiration and for the ramp firing patterns of E2 neurons. Additional CRPG models were developed employing a dual switching neuron that generates two bursts per respiratory cycle to terminate both inspiration and expiration. Although distinctly different each model generates a stable respiratory rhythm and shows physiologically plausible firing patterns of respiratory neurons with and without PSR feedback. Using our models, we analyze the roles of different respiratory neuron types and their interconnections for the respiratory rhythm and pattern generation. We also investigate the possible roles of intrinsic biophysical properties of different respiratory neurons in controlling the duration of respiratory phases and timing of switching between them. We show that intrinsic membrane properties of respiratory neurons are integrated with network properties of the CRPG at three hierarchical levels: at the cellular level to provide the specific firing patterns of respiratory neurons (e.g., ramp firing patterns); at the network level to provide switching between the respiratory phases; and at the systems level to control the duration of inspiration and expiration under different conditions (e.g., lack of PSR feedback).