Elastic and inelastic neutron scattering and magnetization measurements have been used to study peculiarities of the magnetic state in RâT compounds (R=Gd, Er, Tb; T=Ni, Co) below and above magnetic ordering temperatures. A pronounced non-Brillouin shape of the magnetization curves observed in the antiferromagnetic compounds GdâNi and TbâNi above their magnetic ordering temperatures together with earlier reported data about the retention of the magnetic contribution to the total specific heat of GdâT and anomalous behavior of the electrical resistivity above magnetic ordering temperatures are ascribed to the existence of short-range magnetic correlations in the wide temperature range in the paramagnetic state. The persistence of short-range magnetic order up to temperatures greater than 5-6 times the Neel temperature has been revealed by powder neutron diffraction measurements performed for TbâNi and TbâCo. On the other hand, results from inelastic neutron scattering show that the low temperature magnetic excitations are strongly suppressed in both TbâCo and ErâCo. It is suggested that the extended short-range magnetic correlations, which turn out to be an inherent feature of RâT type compounds, are due to the layered crystal structure and to the difference between geometrically frustrated intra-layer exchange interactions and inter-layer exchange.