This paper is devoted to a thorough study of the magnetic properties, both in the de and ac modes, of two-dimensional ferrimagnetic materials. The general formula of the compounds, abbreviated as A(2)M(2)Cu(3), is A(2)M(2) [Cu(opba)](3) . nsolv where A(+) stands for a counter cation (radical cation, alkali-metal or tetraalkylammonium), opba is ortho-phenylenebis(oxamato), M-II is Mn-II or Co-II, and solv is a solvent molecule (Me2SO or H2O). The de magnetic susceptibility data for all compounds down to ca. 50 K are characteristic of two-dimensional ferrimagnets. In the A(2)Mn(2)Cu(3) series, threeclasses of compounds have been distinguished. Class I has a unique representative, A(2)(.)Mn(2)Cu(3), where A(.+) is the radical cation 2-(1-methylpyridinium-4-yl)-4,4,5,5-tetramethylimadozolin- 1-oxyl-3-oxide, the structure of which has already been solved. This compound is a magnet with T-c = 22.5 K. Class II corresponds to compounds with large cations (tetraethyl- and n-tetrabutylammonium). They also behave as magnets with T-c around 15 K. Class III corresponds to compounds with small cations (alkali-metal ions and tetramethylammonium). They behave as metamagnets with a long-range antiferromagnetic ordering in zero field around 15 K, and a field-induced ferromagnetic state. The critical fields are of the order of 0.15 kOe. All the A(2)Co(2)Cu(3) compounds are magnets with T-c around 30 K. Furthermore, the cobalt derivatives show a very strong coercivity, with coercive fields of several kOe at 5 K. They also display a pronounced magnetic after-effect in the ordered phase. In the course of this work several peculiar features have been observed. In particular, the A(2)Mn(2)Cu(3) compounds have been found to present weak but significant negative out-of-phase ac magnetic signals at temperatures just above T-c. All the observed phenomena are discussed and, in particular, a mechanism for the long-range ordering in these two-dimensional compounds has been proposed.