  We propose a criterion for the existence of monotone wavefronts in
non-monotone and non-local monostable diffusive equations of the Mackey-Glass
type. This extends recent results by Gomez et al proved for the particular case
of equations with local delayed reaction. In addition, we demonstrate the
uniqueness (up to a translation) of obtained monotone wavefront within the
class of all monotone wavefronts (such a kind of conditional uniqueness was
recently established for the non-local KPP-Fisher equation by Fang and Zhao).
Moreover, we show that if delayed reaction is local then this uniqueness
actually holds within the class of all wavefronts and therefore the minimal
fronts under consideration (either pulled or pushed) should be monotone.
Similarly to the case of the KPP-Fisher equations, our approach is based on the
construction of an appropriate fundamental solution for associated boundary
value problem for linear integral-differential equation.
