  The paper deals with the decoupling problem of general quasilinear first
order systems in two independent variables. We consider either the case of
homogeneous and autonomous systems or the one of nonhomogeneous and/or
nonautonomous systems. Necessary and sufficient conditions for the partial or
full decoupling of the systems at hand are provided. The conditions involve the
properties of eigenvalues and eigenvectors of the coefficient matrix, and
provide the differential constraints whose integration leads to the decoupling
transformation. Some applications of physical interest are also given.
