Questions concerning stigmatic imaging by means of holographic optical elements (HOEs) are discussed. Several aplanatic systems, in particular holographic doublets, were designed and analyzed. The doublets are generated by both spherical and aspherical recording wavefronts. The imaging properties of a single HOE, single aplanatic HOE, and aplanatic holographic doublets are compared and the superiority of the aplanatic doublets and high degree of astigmatism suppression are demonstrated. The HOE designs and the presented analysis were performed using the HADES computer ray-tracing program.