It is well known that the use of state-equations facilitates the study of dynamical systems. With the availability of standard computer sub-routines, the solution to the state-equations can be easily obtained and the dynamical characteristics of the system may be studied. In this paper the explicit form of the state-variable equations for linear networks has been derived. The networks are considered to comprise resistors, inductors, capicitors, transformers, independent voltage and current sources, and dependent sources. One of the main features of the representation is that, the network contains 'excess' capacitors and inductors. Also the treatments allow mutual inductances to be considered. The method used for the elimination of unwanted variables is described which results in a general form of the state-equations.