The exospheric theory based on the Kappa velocity distribution function (VDF) is used to model the exosphere of the giant planets Jupiter and Saturn. Such Kappa velocity distribution functions with an enhanced population of suprathermal particles are indeed often observed in space plasmas and in the space environment of the planets. The suprathermal particles have significant effects on the escape flux, density and temperature profiles of the particles in the exosphere of the giant planets. The polar wind flux becomes several orders larger when suprathermal electrons are considered, so that the planetary ionosphere becomes then a significant source for their inner magnetosphere. Moreover, the number density of the particles decreases slower as a function of the altitude when a Kappa distribution is considered instead of a Maxwellian one. Two-dimensional maps of density are calculated for typical values of the temperatures. The exospheric formalism is also applied to study the escape flux from the exospheres of Io and Titan, respectively, moons of Jupiter and Saturn. © 2009 Elsevier Ltd. All rights reserved.