A barium deficiency in the"initia1 composition for the synthesis of high-temperature supercondutors (HTSC), i.e. a nominal (RE Ba,-xCu,O,) composition with 0 $ x $ 1 leads to different materials depending on the nature of the rare earth. If the rare earth is 'yltric' (Y, Er, Yb), the resulting compound is a composite YBa,Cu,O, + Y,BaCuO,, whose critical current density depends on the x-value. The determination of the irreversible behaviour by means of AC susceptibility or magnetization measurements shows that in the presence of the 21 1-phase, the intergranular current-density decreases whereas the intragranular current density varies very little. If the rare earth is 'ceric' (Nd, Eu), the lack of barium leads to a quasi single-phased compound. In t h e Nd-case, the critical current density decreases strongly with increasingx. At highx (0.5 < x < 1) and low temperature, t h e magnetization-against-fieid data show paramagnetic behaviour due to the neodymium ions, with an effective momentp.,,,= 1.80 p a . The domain of the reversible behaviour in the (H, r) plane is more extended forNbBaCu0 and EuBaCuO than for YBaCuO.