A method and apparatus for the estimation of maximum friction between a vehicular tire and a road surface via driving dynamics measurements and at least one sensor measuring the road surface, comprising measuring road surface properties via a sensor; measuring the state of motion of a vehicle and a tire and concluding therefrom a momentary maximum friction coefficient when the tire is subjected to a sufficient friction force; storing a maximum friction estimate concluded from the above-mentioned measurements, along with measuring results regarding road surface properties measured at the moment of measurement; when the tire is not subjected to a friction force sufficient for measuring maximum friction, using, as a maximum friction estimate, the previously measured maximum friction estimate, such that an applied selection criterion for the maximum friction estimate is the newness as up-to-date as possible of the measuring result and a consistency of the road surface measuring result.