LET A BE A banach ternary ALGEBRA OVER A SCALAR FIELD R OR C AND X BE A banach ternary A-module. LET S, T AND X BE LINEAR MAPPINGS ON A. WE DEFINE A ternary (S, T , X) -DERIVATION AND A LIE ternary (S, T , X) -DERIVATION. MOREOVER, WE PROVE THE GENERALIZED HYERS-ULAM-RASSIAS STABILITY OF ternary AND LIE ternary (S, T , X) -DERIVATIONS ON banach ternary ALGEBRAS.