The optical hybrid systems, i.e., systems containing the optical elements of different types (diffractive and gradient-index lenses), are considered. The corrective scope of two- and three-element hybrid objectives are investigated. It is shown that the two-element objective may be corrected for all monochromatic third-order aberrations. It is possible in a wide range of relations between optical powers diffractive and gradient-index lenses. It allows us to reduce the space frequency of the structure of the diffractive lens and to decrease the magnitude of the refractive index change of gradient-index lens. In addition, the correction of various fifth-order aberrations may be achieved in this case too. As a result this objective forms the image with high resolution and a wide linear field in the image space. The three-element hybrid objective consists of one diffractive and two gradient-index lenses. This objective has symmetric configuration and unit magnification. It is shown that in such an objective, which is free from all third-order aberrations, it's possible to eliminate simultaneously three out of the four different even fifth-order aberrations. In particular, the validity of this result is conserved if the optical power of the diffractive element is equal to zero. The design of a three-element hybrid objective is given. The resulting designs are compared with homogeneous objectives.