Let X and Y be nonsingular real algebraic varieties. A regulous map from X into Y is a continuous map, which is also rational. Such maps form an intermediate class between regular and semi-algebraic maps, and have some remarkable properties. In particular, they are very usefull in the study of pre-algebraic and algebraic vector bundles. For example, one can show that every pre-algebraic vector bundle on X becomes algebraic after finitely many blowin-ups. Consequently, the Stiefel-Whitney classes of pre-algebraic real vector bundles on X are algebraic.