  The nonclassical transport equation models particle transport processes in
which the particle flux does not decrease as an exponential function of the
particle's free-path. Recently, a spectral approach was developed to generate
nonclassical spectral S$_N$ equations, which can be numerically solved in a
deterministic fashion using classical numerical techniques. This paper
introduces a transport synthetic acceleration procedure to speed up the
iteration scheme for the solution of the monoenergetic slab-geometry
nonclassical spectral S$_N$ equations. We present numerical results that
confirm the benefit of the acceleration procedure for this class of problems.
