  A family of relativistic geometric models is defined as a generalization of
the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator.
It is shown that all these models lead to the usual harmonic oscillator in the
non-relativistic limit, even though their relativistic behavior is quite
different. Among quantum models we find a set of models with countable energy
spectra, and another one having only a finite number of energy levels and in
addition a continuous spectrum.
