A bearing apparatus comprising: a rolling bearing structured such that a plurality of rolling elements held in a holder are rotatably incorporated between a pair of bearing rings (12, 13), a sensor for detecting conditions of a supported rotating shaft or of the rolling bearing, a ring shaped sensor cover secured to one end face in an axial direction of a stationary-side bearing ring, and a ring shaped sensor holding member secured to the sensor cover, wherein the sensor is fitted in a sensor holding groove provided in a determined position along a circumferential direction in the sensor holding member with a determined tightening margin owing to elastic deformation of the sensor holding member, wherein the sensor holding member is formed with a plurality of positioning pins projecting respectively in the axial direction, leaving determined spaces in the circumferential direction, and the sensor cover is formed with a plurality of fitting holes in respective positions corresponding to the plurality of positioning pins, wherein the plurality of positioning pins are fitted in the plurality of respectively corresponding fitting holes, whereby the sensor cover and the sensor holding member are positioned, characterized in that a circuit substrate of the sensor is held between the sensor cover and the sensor holding member, that the plurality of fitting holes are formed in the circumference with projections standing toward the sensor holding member, arranged such that the sensor cover engages the sensor holder or the circuit substrate so that they do not contact other parts than the projections, and that a plurality of positioning pins of the sensor holding member pass through holes provided in the corresponding positions in the circuit substrate, and are inserted in the fitting holes. a rolling bearing structured such that a plurality of rolling elements held in a holder are rotatably incorporated between a pair of bearing rings (12, 13), a sensor for detecting conditions of a supported rotating shaft or of the rolling bearing, a ring shaped sensor cover secured to one end face in an axial direction of a stationary-side bearing ring, and a ring shaped sensor holding member secured to the sensor cover, wherein the sensor is fitted in a sensor holding groove provided in a determined position along a circumferential direction in the sensor holding member with a determined tightening margin owing to elastic deformation of the sensor holding member, wherein the sensor holding member is formed with a plurality of positioning pins projecting respectively in the axial direction, leaving determined spaces in the circumferential direction, and the sensor cover is formed with a plurality of fitting holes in respective positions corresponding to the plurality of positioning pins, wherein the plurality of positioning pins are fitted in the plurality of respectively corresponding fitting holes, whereby the sensor cover and the sensor holding member are positioned, characterized in that a circuit substrate of the sensor is held between the sensor cover and the sensor holding member, that the plurality of fitting holes are formed in the circumference with projections standing toward the sensor holding member, arranged such that the sensor cover engages the sensor holder or the circuit substrate so that they do not contact other parts than the projections, and that a plurality of positioning pins of the sensor holding member pass through holes provided in the corresponding positions in the circuit substrate, and are inserted in the fitting holes.