Piecewise linear systems present almost the same dynamical behaviour as that of general nonlinear systems (limit cycles , homoclinic and heteroclinic orbits, strange attractors, ...).\\\\ In order to carry out a complete study of picewise linear systems, some canonical forms have been introduced in several works. In practice, many nonlinear systems can be adequately modelled by continuous piecewise linear systems separated by one or two parallel hyperplanes, splitting the phase space in $ \\mathbb{R}^{3} $ i n to different linear dynamic regions. In this case, the canonical forms which take advantage of some concepts from We consider the existence of periodic orbits in a Firstly , we describe the dynamical behavior of a non-generic piecewise linear system which has two equilibria and one two-dimensional invariant manifold foliated by periodic orbits . Next, if possible, some systems in the family are described as perturbations of the non-generic cases studied, and then, the dynamical behavior of the perturbed systems is analyzed. The aim of this work is to study the periodic orbits of the continuum that persist under a piecewise linear perturbation of the system . According to the above ideas, we will present here some interesting situations, showing periodic orbits when the involved linear parts share a pair of imaginary eigenvalues. In the bounded case, the corresponding invariant manifold turns out to be a topological sphere that under perturbations yields a very complex behaviour, as it may be deduced from some Poincare sections of the flow. \\\\ In order to analyze this situation , we build a real function of real variable whose zeros are related to the limit cycles that remain after the perturbation . By using this function , we state some results of existence and stability of limit cycles in the perturbed system , as well as results of bifurcation of limit cycles . The techniques presented are similar to the Melnikov theory for smooth systems and the method of averaging . \\\\ Finally, we state and prove our main results about the existence, stability and bifurcations of limit cycles in our system by means of the properties of Melnikov function.