It is demonstrated that there exist ternary Moufang loops that are di erent from ternary groups. Let (K;+;
; 1) be an associative ring (not necessary commutative) which has characteristic 3, i.e., x + x + x = 0 for all x 2 K. By K0(
) we denote an abelian subgroup of the group K(
). Here K = Knf0g. The map x ! s
x for all x 2 K is a permutation for any s 2 K0. Moreover, we require that s2 = 1 for all s 2 K0. In particular case K = Z3 is a ring of residues modulo 3. On the set Q = K0  K = f< s; k >j s 2 K0; k 2 Kg we de ne the following ternary operation A( < s1; x1 >;< s2; x2 >;< s3; x3 >) =< s1s2s3; s2x1 + s3x2 + s1x3 > (1) for all s1; s2; s3 2 K0; x1; x2; x3 2 K. Algebra Q(A) with operation de ned on the set Q = K0  K by the formula (1) is a ternary non-commutative Moufang loop that is not a ternary group. Example of ternary commutative Moufang loop that is not a ternary group is also constructed.