Device for determining the straightness of hollow cylindrical surfaces and partial surfaces thereof, and the three-dimensional orientation of several hollow cylindrical surfaces or partial surfaces with reference to at least one of axial parallel offset and angular offset relative to one another. A transmitting/receiving device and a reflector/receiving device are provided which are swingable essentially without play over a respective hollow cylindrical surface or partial hollow cylindrical surface. The transmitting/receiving device has at least one transmitter for emitting light beams and at least one receiver for receiving and for measuring an incidence position of the light beams. The reflector/receiving device has at least one partially-reflective optical element for partial reflection of light beams and at least one receiver for receiving and for measuring an incidence position of a portion of the light beams. The relationship between circular lines produced on the detectors in different phases of measurement is used.