We study particle acceleration and radiation in the jets of active galactic nuclei (AGN). Although the jet outflow is relativistic, we make the assumption that electrons are accelerated in a shock-front that is moving non-relativistically in the jet frame. Acceleration and energy losses are treated self-consistently through a kinetic equation which also includes particle injection and escape. As a first step we consider only losses from inverse Compton scattering (ICS) of the high energy electrons on the disc photons. The disc model we adopt is of a standard, multi-temperature Shakura-Sunyaev type. The particle distribution function resulting from the solution of the kinetic equation, is convolved with the single particle emissivity for ICS using the full Klein-Nishina cross-section and the emitted spectrum at each height of the jet is obtained. The total spectrum is calculated by integrating the contribution from all heights and then it is compared to high-energy AGN observations.