  It is shown that three-dimensional nonparaxial beams are described by the
oblate spheroidal exact solutions of the Helmholtz equation. For the first
time, their beam behaviour is investigated and their corresponding parameters
are defined. Using the fact that the beam width of the family of paraxial
Gaussian beams is described by an hyperbola, the connection between the
physical parameters of nonparaxial spheroidal beam solutions and those of
paraxial beams is formally stablished. These results are also helpful to
investigate the exact vector nonparaxial beams.
