In this article we look into stability properties of strongly autonomous n-D systems, i.e. systems having finite-dimensional behaviour. These systems are known to have a first-order representation akin to 1-D state-space representation; we consider our systems to be already in this form throughout. We first define restriction of an n-D system to a 1-D subspace. Using this we define stability with respect to a given half-line, and then stability with respect to collections of such half-lines: proper cones. Then we show how stability with respect to a half-line, for the strongly autonomous case, reduces to a linear combination of the state representation matrices being Hurwitz. We first relate the eigenvalues of this linear combination with those of the individual matrices. With this we give an equivalent geometric criterion in terms of the real part of the characteristic variety of the system for half-line stability. Then we extend this geometric criterion to the case of stability with respect to a proper cone. Finally, we look into a Lyapunov theory of stability with respect to a proper cone for strongly autonomous systems. Each non-zero vector in the given proper cone gives rise to a linear combination of the system matrices. Each of these linear combinations gives a corresponding Lyapunov inequality. We show that the system is stable with respect to the proper cone if and only if there exists a common solution to all of these Lyapunov inequalities.