We report magnetic susceptibility, specific heat and muon spin relaxation (μSR) experiments on the triangular antiferromagnet La 2 Ca 2 MnO 7 which develops a genuine two-dimensional (2D), three-sublattice [Formula: see text] magnetic order below T N = 2.8 K. From the susceptibility and specific heat an estimate of the exchange interaction is derived. A value for the spin-wave gap is obtained from the latter data. The analysis of a previously reported inelastic neutron scattering data yields values for the exchange and spin-wave gap compatible with the results obtained from macroscopic measurements. An appreciable entropy is still missing at 10 K that may be ascribed to intense short-range correlations. The critical paramagnetic fluctuations extend far above T N , and can be partly understood in terms of two-dimensional spin-wave excitations. While no spontaneous μSR field is observed below T N , persistent spin dynamics is found. Short-range correlations are detected in this temperature range. Their relation to a possible molecular spin substructure and the observed exotic spin fluctuations is discussed.