AbstractIt is shown that if there equivalently exist the virtual resistive elements in parallel with the inductive elements of the over‐normal tree of a given linear active network or in series with the capacitive elements of the corresponding co‐tree, an increase in the number of state variables arises. It is also shown that when a virtual resistor equivalently appears in parallel with the distinct resistor in a tree or in series with the distinct resistor in the co‐tree, a decrease in the number of state variables may arise. This is, however, a rare case in the usual types of network.Two algebraic methods for obtaining the state equation of linear active networks are presented. One is useful for the networks in which the decrease in the number of state variables does not arise. From the other, the output equation for the required variables is obtained at the same time as the state equation. Further, the initial values are simply determined without iteration in many