The object of the present study is to evaluate the performances of various microcanonical molecular dynamics algorithms. To do so, the divergence times and energy fluctuations are discussed for a model system, i. e. a three-dimensional Lennard-Jones system under various conditions of number densities and temperatures. The results of the evaluations of superiority or inferiority of algorithms are as follows. The velocity Verlet, leapfrog, and Beeman algorithms are significantly superior to the other algorithms such as the 4-value Gear algorithm since a system does not diverge and the energy conservation law is reasonably satisfied for much larger time intervals. Although these three algorithms show approximately the same performance concerning the properties of divergence times and energy fluctuations, we can conclude that the velocity Verlet algorithm is the most suitable for molecular dynamics simulations of flow problems, since this algorithm is easy to use, requires less computer memory, and evaluates molecular positions and velocities at the same time steps.