A rolling element having comprises an inner ring, an outer ring and a series of rolling elements which are in contact with the raceways of the rings, an ultra-low viscosity fluid being present in the contacts having a kinematic viscosity .nu.=(.eta..sub.o/.rho.) of less than 2 mm.sup.2/s, wherein the surfaces of the rings and the rolling elements have asperities which can have solid-to-solid contact during operation of the bearing. A factor D.sub.q is defined which is equal to (I) whereby the solid-to-solid contact of the asperities is reduced by selecting such design parameters and operating conditions of the bearing that D.sub.q is in the range from 8.0.times.10.sup.-6 mrad s.sup.1/2 to 1.36.times.10.sup.-4 mrad s.sup.1/2.