The invention relates to a device for grinding a portion of the surface 2 of a product, in particular a metal product 4, that is in particular uneven and yielding under a pressing force, comprising a holding device 5, holding a grinding stone 8 with a planar grinding surface 16, comprising a device 6, carrying the holding device 5, for placing the grinding stone 8 onto the portion of the surface 2, and comprising a device 6 for moving the grinding stone 8 and the product 4 in relation to one another. According to the invention, the grinding stone 8 is cardanically mounted in the holding device and the holding device 5 is held on the device 6 for placing in such a way that, in a projection onto the surface 3, the pivoting axes X, Y of the cardanic mounting are pivoted from a position in which the one pivot axis Y is aligned transversely and the other pivot axis X is aligned axially parallel in relation to the momentary direction L of the relative movement together about a grinding angle beta that is > 0° and
