X-ray magnetic circular dichroism (XMCD), small-angle neutron scattering (SANS), and ac magnetic susceptibility (chiac) measurements as a function of temperature and magnetic field on the Laves phase compound ErCo2 are presented. The results allow one to investigate in detail the ErCo2 paramagnetic phase. The XMCD data reveal an extended region on the phase diagram where the net magnetization of the Er and Co sublattices are oriented in opposite directions at temperatures well above the ferrimagnetic ordering temperature. The complete characterization of the phenomenon by means of SANS and chiac measurements allows us to propose the occurrence of short-range magnetic order, which we described and systematically studied and which we denote as parimagnetism. The origin of the parimagnetism is analyzed in terms of the different magnetic interactions present in the system. We conclude that parimagnetism in ErCo2 is driven by the formation of Co magnetic clusters which are ferromagnetically coupled within the paramagnetic phase.