A stochastic equation, differing from the Langevin equation by the addition of a second order derivative in the fictitious time, is studied for numerical simulations of euclidean field theories. The simplest discretization in the time direction (step size ϵ) is shown to lead to O(ϵ 2) errors, to be compared with O(ϵ) errors in the simplest, Euler-discretized Langevin equation. It was essentially because of this that the hyperbolic equation was found, from extensive numerical experiments on the XY model, to be far more efficient than the Langevin equation: for equal systematic errors, sweep-sweep correlation times were found to be much less in the hyperbolic case. Relations to other algorithms are also discussed.