We will present sufficient conditions for the Fredholm property of Wiener-Hopf plus and minus Hankel operators with different Fourier matrix symbols in the C∗ -algebra of semialmost periodic elements. In addition, under such conditions, we will derive a formula for the sum of the Fredholm indices of these Wiener-Hopf plus Hankel and Wiener-Hopf minus Hankel operators. Some examples are provided to illustrate the results of the paper.