The principle and experimental realization of X-ray phase-contrast in computer assisted microtomography (mu CT) at the micrometer resolution level is described. The camera used is a modification of a setup previously developed by us for attenuation-contrast mu CT using synchrotron X rays (SR)(1). Phase detection is accomplished by employing the X-ray interferometer. By using X-ray phase contrast it is possible to image structural details in low-Z biological tissues much better than with absorption contrast (Z: Atomic Number). The advantage of phase over attenuation contrast is not limited to light elements nor to low X-ray energies. Examples of applying phase contrast mu CT to the structural investigation of rat trigeminal nerve are given.