In this series of papers, we develop a two-fluid model for VLBI jets. The idea is that the jet itself is non- or mildly-relativistic (electrons and protons), while the radiating blobs are relativistic electron-positron "clouds" moving on helical paths wrapped around the jet. In this work, the emphasis is on the physical description of the clouds, and not on the structure or origin of the trajectory. In the simple case where the magnetic field is uniform and homogeneous accross the cloud, and the properties of the cloud are constant, the present paper shows synthetic maps of VLBI jets in different configurations, as well as the variation of different observational parameters along the trajectory.