  We show that it is possible to obtain credible static anisotropic spherically
symmetric matter configurations starting from known density profiles and
satisfying a nonlocal equation of state. These particular types of equation of
state describe, at a given point, the components of the corresponding
energy-momentum tensor not only as a function at that point, but as a
functional throughout the enclosed configuration. To establish the physical
plausibility of the proposed family of solutions satisfying nonlocal equation
of state, we study the constraints imposed by the junction and energy
conditions on these bounded matter distributions.
  We also show that it is possible to obtain physically plausible static
anisotropic spherically symmetric matter configurations, having nonlocal
equations of state\textit{,}concerning the particular cases where the radial
pressure vanishes and, other where the tangential pressures vanishes. The later
very particular type of relativistic sphere with vanishing tangential stresses
is inspired by some of the models proposed to describe extremely magnetized
neutron stars (magnetars) during the transverse quantum collapse.
