Apparatus (or method) for estimating a gripping characteristic of a vehicle wheel of a vehicle on a ground contact surface includes first input section (or step), a second input section (or step) and an output section (or step). The first input section sets a first input which is a ratio of a first wheel force acting on the vehicle wheel in the ground contact surface in a first direction, and a first wheel slip degree. The second input section sets a second input which is a ratio of a second wheel force acting on the vehicle wheel in the ground contact surface in a second direction, and a second wheel slip degree of the vehicle wheel. The output section determines, from the first and second inputs, an output which is a grip characteristic parameter indicative of the gripping characteristic of the vehicle wheel.