  The dynamical symmetries of the two-dimensional Klein-Gordon equations with
equal scalar and vector potentials (ESVP) are studied. The dynamical symmetries
are considered in the plane and the sphere respectively. The generators of the
SO(3) group corresponding to the Coulomb potential, and the SU(2) group
corresponding to the harmonic oscillator potential are derived. Moreover, the
generators in the sphere construct the Higgs algebra. With the help of the
Casimir operators, the energy levels of the Klein-Gordon systems are yielded
naturally.
