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Monte Carlo simulations of two-dimensional fluids with a truncated Lennard-Jones interaction in the NVT ensemble are analysed with a block density distribution technique, for N= 256 and N= 576 particles. It is shown that below T c (critical temperature) the block density function develops a well defined two-peak structure. From the locations of these two peaks the densities of the two coexisting phases can be reliably estimated. In the one-phase region the width of the single-peak is used to extract information on the compressibility, by extrapolating the results for finite block size versus inverse block linear dimension to the thermodynamic limit. Studying the temperature dependence of the fourth-order cumulant of the block density distribution at the critical density for various block sizes, the location of the critical temperature is found from the intersection of the cumulants, just as in the simpler case of Ising models. The …