NVT simulations on Lennard-Jones (L-J) systems near the gas-liquid critical point were performed by a direct approach. As a result, the two necessary conditions for simulating the systems in accordance with the thermodynamic limit were proposed: (i) L/xi greater than or similar to 20 (L: the box-length, xi: the correlation length), (ii) the total time of evolution, t(E) > 500 L-J units, for xi approximate to 3.5. The proposed conditions are probably very close to the sufficient ones. The influence of finite-size effects on pressure and density of small systems was qualitatively predicted. The prediction was confirmed by the simulations but only for L markedly lower than the length of typical critical wave, 2 pi xi. For L markedly higher, the evolutions were dominated by an effect called here the instability effect. The effect became negligible just when the condition for L/xi was fulfilled. The xi (0)' constant for L-J fluid was estimated from direct measurements of xi to be 0.27 +/- 0.02 (L-J units). The thermodynamic parameters of the critical point, obtained from extrapolation, were in agreement with the results of other authors. The Be exponent was estimated from minimization for a high range of temperatures to be 0.346. A comparison of the efficiency of NVT and NpT methods was also performed and no distinct differences were noted.