Two implementations of the backward Euler method for simulating molecular fluids are compared with Brownian dynamics and molecular dynamics simulations of a single diatomic molecule, liquid argon, a single butane molecule, and liquid butane. By comparison with standard molecular dynamics results, backward Euler simulations give different thermodynamic properties for liquids; predict liquid structures which are too solidlike; and incorrectly represent dynamical relaxation processes. The backward Euler methods allows longer time steps to be used in simulations at the cost of an energy minimization at every time step. Even when time steps more than 20 times larger than that required for energy and momentum conservation are used, neither implementation of the backward Euler algorithm is more accurate than standard molecular dynamics calculations with the same time step. We conclude that the new methods offer no computational advantages over more usual methods for simulating molecular fluids and that they often predict incorrect results.