We found that in TmCo2 the molecular field does not exceed the critical value necessary to induce long-range magnetic order in the Co d-electron subsystem, which is in contrast to the other heavy RCo2 compounds. Below Tc=3.8 K a first-order magnetic phase transition at 3.4 K exists, which is due to a rearrangement of the Tm 4f magnetic moments. When substituting Tm by Gd long-range magnetic order appears in the Co d subsystem. The onset of the magnetic order in the d-electron subsystem can most clearly be seen from thermal expansion measurements. There is an increasing positive volume anomaly with increasing Gd content below Tc. The estimated magnetostriction constant lambda 111 of TmCo2 is -4.1*10-3, in agreement with the single-ion model. Pronounced discontinuities at Tc are characteristic for the transport properties (resistivity and thermopower) for TmCo2 as well as for the pseudobinary Tm1-xGdxCo2 compounds. At elevated temperatures the physical properties of all these compounds are dominated by spin fluctuations.