Parasitic resistances and offset voltage sources of power switches are included in the averaged-circuit models of an actual switching part of PWM transformerless converters which operate in a continuous conduction mode. The actual switching part is divided into the ideal switching part and its parasitics. It is shown that the ideal switching part can be modeled by one of 24 equivalent averaged circuits, each consisting of a dependent current source and a dependent voltage source. The parasitics are averaged using the principle of energy conservation. The obtained nonlinear large-signal model of the actual switching part can be placed into the buck, boost, and buck-boost topologies leading to averaged-circuit models of power stages. Linearization of the model around a dc operating point results in dc and small-signal models of the converters. Reflection rules are established which can be used to simplify the circuit models. The proposed method is illustrated by modeling the PWM boost converter.