Abstract: We present in this note a multi-dimensional mesh refinement technique that is adaptive both in time and space. This technique is based on the principle of maintaining a C.F.L. ratio constant throughout the time calculus and is designed in its actual form for schemes modeling hyperbolic problems. To test it, we study numerically two hyperbolic model problems in two dimensions of space. The first is an advection equation, the second is the free wave equation. The goal of these computations is to retrieve the results computed with the same numerical scheme and C.F.L. ratio over a regular space time grid of the thinner mesh used by our adaptive mesher.