  We obtain novel periodic as well as hyperbolic solutions of an
Ablowitz-Musslimani variant of the coupled nonlocal, nonlinear Schr\"odinger
equation (NLS) as well as a coupled nonlocal modified Korteweg-de Vries (mKdV)
equation which can be re-expressed as a linear superposition of the sum or the
difference of two hyperbolic or two periodic kink or pulse solutions. Besides,
we also discuss some of the other solutions admitted by these coupled
equations. These results demonstrate that the notion of the superposed
solutions extends to the coupled nonlocal nonlinear equations as well.
