The behavior of charged particles near X-type magnetic neutral lines is investigated. The magnetic field is taken to be hyperbolic and time stationary, with a uniform electric field perpendicular to the magnetic field. The general properties of the orbits of noninteracting particles in that field geometry are examined. Approximate analytic solutions to the orbit equations are derived by considering a magnetic-insulation picture where there is a hole in the magnetic insulation around the neutral line. Scaling laws for the dependence of the energy gain on strengths of the magnetic and electric fields are derived. The kinetic-energy distribution function for accelerated particles is derived for particles flowing past the neutral line. These analytic derivations are supported by computer simulations, in which the relativistic equations of motion for single test particles are numerically solved and the orbits and kinetic-energy gains of the particles are obtained. A number of simulations were performed and one parameter at a time was varied. Applications of the results to magnetic-neutral-line regions in space physics and astrophysics are possible.