  A factorization theory is proposed for Wiener-Hopf plus Hankel operators with
almost periodic Fourier symbols. We introduce a factorization concept for the
almost periodic Fourier symbols such that the properties of the factors will
allow corresponding operator factorizations. Conditions for left, right, or
both-sided invertibility of the Wiener-Hopf plus Hankel operators are therefore
obtained upon certain indices of the factorizations. Under such conditions, the
one-sided and two-sided inverses of the operators in study are also obtained.
