  This article addresses linear hyperbolic partial differential equations and
pseudodifferential equations with strongly singular coefficients and data,
modelled as members of algebras of generalised functions. We employ the
recently developed theory of generalised Fourier integral operators to
construct parametrices for the solutions and to describe propagation of
singularities in this setting. As required tools, the construction of
generalised solutions to eikonal and transport equations is given and results
on the microlocal regularity of the kernels of generalised Fourier integral
operators are obtained.
