An imaging tomography apparatus, in particular an x-ray tomography apparatus or an ultrasound tomography apparatus, has a stationary unit with a sensor for measurement of an out-of-balance condition of an annular data acquisition device rotatable around a patient opening in the stationary device. Compensation weights for compensation of the out-of-balance condition are provided on the data acquisition device. To simplify the balancing procedure, the compensation weights are disposed in two parallel planes axially separated from one another, and in each plane at least three compensation weights are fashioned as chambers that can be filled with a fluid. At least two of the chambers are connected with one another via at least one conduit for fluid transfer therebetween exchange.