  We analyze nonclassical correlations between outcomes of measurements
conducted on two spatial radiation modes. These correlations cannot be
simulated with statistical mixtures of coherent states or, more generally, with
non-negative phase-space functions of quantum states and measurements. We argue
that nonclassical correlations are naturally related to Bell nonlocality, the
former being a more general class of quantum correlations. Indeed, it is known
that local realistic as well as noncontextual models correspond to non-negative
solutions to a system of linear equations for the joint probability
distributions of all observables. We demonstrate that nonclassical correlations
correspond to a particular solution to this system, which may have negative
values even if local realism is not violated. A modification of Bell
inequalities enables us to test such correlations. At the same time, our
approach leads to a formulation of Bell inequalities applicable also to
continuous variables. The results are illustrated with two-mode squeezed vacuum
states and with hybrid entangled states (Schr\"odinger-Cat states), one mode
being analyzed by balanced and the other one by unbalanced homodyne detection.
