Spherical head assembly for attaching an optical and / or electronic device to a stander with an adjustability in at least two degrees of freedom, which has a first part that can be releasably connectedto the stander and a second part which is provided with a support element for the releasable connection of the device to be held thereby, and one of the two parts is a spherical head (20, 100) that has a body (21, 99) which has at least in part a spherical shape, and the other part comprises a cavity formed as a spherical segment which encircles the spherical head (20, 100) at least in part and is fitted thereto, and comprises an adjusting means for coupling the two parts together and releasing the same coupling, and in the initial position of intended use the held device is adjusted in horizontal or almost horizontal position. In the second part a groove (24, 108) is provided that has a vertical central plane and extends along the largest diameter of the spherical segment, and on the first part a circularly symmetrical stud (25, 103) is provided at a position that corresponds to the vertical diameter of the spherical segment and the stud (25, 103) can be fitted in the groove (24, 108), and in the fitted position the stud (25, 103) allows the displacement of the two parts along the groove (24, 108), and the stud (25, 103) allows the turning of the two coupled spherical fitted segments around the vertical axis of the stud (25, 103) at each of the adjusted positions, and the adjusting means is arranged on that one of the two parts which has the spherically shaped cavity, and when the position of two parts are fixed the adjusting means presses the cavity to the spherical body (21, 99).