A gantry-type positioning device includes first and second cross members. Two linear guides are disposed parallel to each other on a base and support the first and second cross members such that the cross members are movable in a first direction. A Y-carriage has a functional element and is supported on the first cross member such that the Y-carriage and the functional element are movable in a second direction. A position-measuring device is disposed on the second cross member and the Y-carriage such that a position of the Y-carriage relative to the second cross member is detectable. A Z-carriage supports the functional element such that the functional element is movable relative to the Y-carriage in a third direction. A further position-measuring device is disposed on the Y-carriage and the functional element such that a position of the functional element relative to the Y-carriage is detectable.