The conventional form of Gaussian beam propagation in inhomogeneous media is based on paraxial approximation in an orthogonal ray-centered coordinate system. However, phase-space spectral distributions of wave fields require beam solutions in which the initial Gaussian distribution is given on a plane which is generally inclined to the beam propagation direction. Thus, the conventional paraxial approximation is not valid for large-angle spectral components. The current research is dealing with paraxial beam solutions in inhomogeneous media, which are asymptotically valid for all angles of propagation. By applying a novel non-orthogonal ray-centered coordinate system to the inhomogeneous wave equation and using asymptotic (paraxial) considerations, the wave equation is reduced into a new form of a Parabolic wave equation. Solutions to this equation, form a new kind of beam waveobjects which serve as building blocks for phase-space representations. The characteristics of these wave fields are investigated, as well as the novel wave phenomena associated with them.