A device for the non-invasive detection of apneae or hypopneae in a patient. This apparatus collects the patient's endocardial acceleration using an external acceleration sensor (12) able to be maintained in contact with the patient's thoracic wall (10). An analysis is made to determine at least one parameter that is function of collected endocardial acceleration and to conditionally deliver an apnea or hypopnea alert signal as a function of the value taken by this parameter. This parameter can notably be a function of one and/or the other of the two endocardial acceleration peaks over one given heart cycle, the first peak (PEA I) corresponding to the ventricular isovolumetric contraction phase and the second peak (PEA II) to the ventricular isovolumetric relaxation phase.