  In this paper we construct several supersymmetric theories, including SU(N)
gauge theory, on AdS_5 background. We discuss the proper definition of the
Killing equation for the symplectic Majorana spinors required in AdS_5
supersymmetric theories. We find that the symplectic Killing spinor equation
involves a matrix M in the USp(2N) indices whose role was not recognized
previously. Using the correct Killing spinors we explicitly confirm that the
particle masses in the constructed theories agree with the predictions of the
AdS/CFT correspondence. Finally, we establish correct O(d-1,2) isometry
transformations required to keep the Lagrangian invariant on AdS_d.
