This work discusses techniques for electrical network digital simulation, emphasizing real time operation. The networks contain transmission lines as distributed elements and RLC elements as lumped parameters, although many of the results are not restricted to these elements. Transmission line modeling is considered first, comparing two of the methods found in literature from the real time simulation point of view. The convenience of their use is subject of analysis, leading, later on, to suggest a blend of approaches for real time simulation. In the sequence of the work, it is introduced a new numerical integration algorithm, based on network state space description and multirate digital filtering. The new integration method reduces the simulation computational complexity while simultaneously improving its accuracy. Next, the focus is on numerical oscillations caused by the Trapezoidal Integration approach in some network configurations. It is presented a method to identify electrical network configurations that might generate numerical oscillations in their digital counterparts. The method is a result of both, network and digital signal theory. Conventional and new techniques are applied in order to eliminate the numerical oscillations. The new multirate approach improves convetional techniques results, while properly used eliminates by itself the numerical oscillations. Some power systems network illustrative cases are included, using the new integration method and the proposed digital transmission line model. It is shown that this combination produces improved performance, final accuracy and reduced computational effort, resulting appropriate for real time simulations.