Currently, there are an increasing number of power electronics converters in electrical grids, performing the most diverse tasks, but most of them, work as constant power loads (CPLs). This work presents a sufficient condition for the local stability of dc linear time-invariant circuits with constant power loads for all the possible equilibria (depending on the drained power) of the systems. The condition is shown as a method with successive steps that should be met. Its main step is expressed as a linear matrix inequality test which is important for easiness of verification reasons. The method is illustrated with two examples: a single-port RLC circuit connected to a CPL and a two-port linear dc circuit connected to two CPLs.