  Wiener-Hopf plus Hankel operators $W(a)+H(b):L^p(\mathbb{R}^+)\to
L^p(\mathbb{R}^+)$ with generating functions $a$ and $b$ from a subalgebra of
$L^\infty(\mathbb{R})$ containing almost periodic functions and Fourier images
of $L^1(\mathbb{R})$-functions are studied. For $a$ and $b$ satisfying the
so-called matching condition
  \begin{equation*} a(t) a(-t)=b(t) b(-t), \quad t\in \mathbb{R},
\end{equation*} we single out some classes of operators $W(a)+H(b)$ which are
subject to Coburn-Simonenko theorem.
