  A new integrable class of quantum models representing a family of different
discrete-time or relativistic generalisations of the periodic Toda chain (TC),
including that of a recently proposed classical close to TC model [7] is
presented. All such models are shown to be obtainable from a single ancestor
model at different realisations of the underlying quantised algebra. As a
consequence the $(2\times 2)$ Lax operators and the associated quantum
$R$-matrices for these models are easily derived ensuring their quantum
integrability.
  It is shown that the functional Bethe ansatz developed for the quntum TC is
trivially generalised to achieve seperation of variables also for the present
models.
