Este articulo aparecio publicado en la revista Signal Processing Letters del IEEE en Septiembre de 1996 Articulo premiado por el Fondo de Reconocimiento de la Actividad Academica. So far, the applicability of locally monotonic regression has been limited by the high computational costs of the available algorithms that compute them. We present a powerful theoretical result about the nature of these regressions. As an application, we give an algorithm for the computation of lomo-3 regressions which reduces the complexity of the task, from exponential to polynomial.