In a process and apparatus for controlling the attitude of a spacecraft, drive signals for driving attitude control units of the spacecraft are generated based on control unit signals related to the three principle axes of a spacecraft oriented coordinate system, using the rule k=B.sup.I e+cu.sub.2. The drive matrix B.sup.I, a definite vector u.sub.2 and the constant c result from the application of a matrix decomposition according to the Singular Value Decomposition (SVD) method to a nozzle matrix B. The latter matrix contains as elements, the momentum and force vectors which can be generated by the attitude control units, and the drive matrix B.sup.I is multiplied directly with the vector e derived from the axis-related control unit signals.