  Vector beams display varying polarisation over planes transversal to their
direction of propagation. The variation of polarisation implies that the
electric field cannot be expressed as a product of a spatial mode and its
polarisation. This non-separability has been analysed for particular vector
beams in terms of non--quantum entanglement between the spatial and the
polarisation-degrees of freedom, and equivalently, with respect to the degree
of polarisation of light. Here we demonstrate theoretically and experimentally
that Mathieu-Gauss vector modes violate a Bell-like inequality known as the
Clauser-Horn-Shimony-Holt-Bell (CHSH-Bell) inequality. This demonstration
provides new insights into that fact that a more general class of vector modes
with elliptical symmetry also violate Bell inequalities.
