  In recent years, an extensive survey on various wave equations of
relativistic quantum mechanics with different types of potential interactions
has been a line of great interest. In this regime, special attention has been
given to the Dirac equation because the spin-1/2 fermions represent the most
frequent building blocks of the molecules and atoms. Motivated by the
considerable interest in this equation and its relativistic symmetries (spin
and pseudospin) in the presence of solvable potential model, we attempt to
obtain the relativistic bound states solution of the Dirac equation with double
ring-shaped Kratzer and oscillator potentials under the condition of spin and
pseudospin symmetries. The solutions are reported for arbitrary quantum number
in a compact form. the analytic bound state energy eigenvalues and the
associated upper- and lower-spinor components of two Dirac particles have been
found. Several typical numerical results of the relativistic eigenenergies have
also been presented. We found that the existence or absence of the ring shaped
potential potential has strong effects on the eigenstates of the Kratzer and
oscillator particles with a wide band spectrum except for the
pseudospin-oscillator particles where there exist a narrow band gap.
