The phase diagrams of the mixed spin-1 and spin-2 Blume-Capel Ising ferromagnetic system (J > O) with two crystal-field interactions, D-A for spin-1 and D-B for spin-2, is studied on the Bethe lattice by using the exact recursion equations. The exact expressions of the order-parameters for the sublattices with spin-1 and spin-2, and the Curie temperature and the free energy of the system are obtained in terms of the recursion relations. The phase diagrams on the (kT(c)/J,D-A/J) and (kT(c)/J,D-B/J) planes are studied for selected values of D-B/J and D-A/J, respectively, for the coordination numbers q = 3,4, and 6. Besides the second-order phase transition lines, the lines of the first-order phase transitions terminating either at a tricritical point or at an isolated critical point are found. (C) 2004 Elsevier B.V. All rights reserved.