The approximately analytical bound state solutions of the l-wave Klein-Gordon and k-state Dirac equations with the mixed Eckart potentials are carried out by a proper approximation to the centrifugal term. The analytical radial wave functions of the l-wave Klein-Gordon and k-state Dirac equations with the mixed Eckart potentials are presented and the corresponding energy equations are derived. Two special cases for k = 1 and for k = 1 and β = 0 are studied briefly. Finally, we also verify the rationality of this approximation.