Two general mathematical methods are discussed which may be used to study the effects of electric and/or magnetic deflection fields on electron beams. The basic equations for the ``path method'' are the equations of motion of Newton or Euler-Lagrange. The ``iconal method'' makes use of certain properties of the Hamiltonian function. These methods are then applied to describe the action of balanced, two-dimensional electric deflection fields on electron beams. It is shown that both methods yield essentially the same results. Expressions are derived describing the magnitude of deflection and the distortions of an electron beam. Only the path method is used in a similar investigation of magnetic-type deflection fields.