  The Generalized Parton Distributions (GPDs) of the nucleon are analyzed
within the relativistic constituent quark model formulated on the light-front.
It is shown that the matrix elements of the plus component of the one-body
vector current are plagued by spurious effects related to the dependence on the
hyperplane where the nucleon wave function is defined in terms of its
constituents. The physical GPDs can be extracted only from the matrix elements
of a transverse component of the one-body current. The loss of the
polinomiality property is then related to the neglect of the pair creation
process for non-vanishing values of the skewness. The need of implementing
effective many-body currents corresponding to the Z-graph is stressed and a
possible approach to achieve such a goal is proposed.
