An accelerator complex for hadron therapy based on a chain of cyclotrons is under development at JINR (Dubna, Russia), and the corresponding conceptual design is under preparation. The complex mainly consists of two superconducting cyclotrons. The first accelerator is a compact cyclotron used as an injector to the main accelerator, which is a six-fold separated sector machine. The facility is intended for generation of protons and carbon beams. The H 2 + and 12 C 6 + ions from the corresponding ECR ion sources are accelerated in the injector-cyclotron up to the output energy of 70 MeV/u. Then, the H 2 + ions are extracted from the injector by a stripping foil, and the resulting proton beam with the energy of 70 MeV is used for medical purposes. After acceleration in the main cyclotron, the carbon beam can be either used directly for therapy or introduced to the main cyclotron for obtaining the final energy of 400 MeV/u. The basic requirements to the project are the following: compliance to medical requirements, compact size, feasible design, and high reliability of all systems of the complex. The advantages of the dual cyclotron design can help reaching these goals. The initial calculations show that this design is technically feasible with acceptable beam dynamics. The accelerator complex with a relatively compact size can be a good solution for medical applications. The basic parameters of the facility and detailed investigation of the magnetic system and beam dynamics are described. [ABSTRACT FROM AUTHOR]