The CPLEAR collaboration has constructed a detector at CERN for an extensive programme of CP-, T- and CPT-symmetry studies using K 0 and K 0 produced by the annihilation of p's in a hydrogen gas target. The K 0 and K 0 are identified by their companion products of the annihilation K ± π which are tracked with multiwire proportional chambers, drift chambers and streamer tubes. Particle identification is carried out with a liquid Cherenkov detector for fast separation of pions and kaons and with scintillators which allow the measurement of time of flight and energy loss. Photons are measured with a lead/gas sampling electromagnetic calorimeter. The required antiproton annihilation modes are selected by fast online processors using the tracking chamber and particle identification information. All the detectors are mounted in a 0.44 T uniform field of an axial solenoid of diameter 2 m and length 3.6 m to form a magnetic spectrometer capable of full on-line reconstruction and selection of events. The design, operating parameters and performance of the subdetectors are described.