The Generalized Coherent State Model, proposed previously for a unified description of magnetic and electric collective properties of nuclear systems, is extended to account for the chiral like properties of nuclear systems. To a phenomenological core described by the GCSM a set of interacting particles are coupled. Among the particle-core states one identifies a finite set which have the property that the angular momenta carried by the proton and neutron quadrupole bosons and the particles respectively, are mutually orthogonal. All terms of the model Hamiltonian satisfy the chiral symmetry except for the spin-spin interaction. The magnetic properties of the particle-core states, where the three mentioned angular momenta are orthogonal, are studied. A quantitative comparison of these features with the similar properties of states, where the three angular momenta belong to the same plane, is performed.
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