Abstract: Sequences over the alphabet {-1,0,1} are called ternary sequences. Including the conventional ternary complementary sequences as special cases, the aperiodic ternary Z-complementary sequences are brought forward and may be used as an alternative of ternary complementary sequences in many engineering applications. The elementary transformations on ternary sequences and elementary operations on ternary Z-complementary sets are proposed. It is shown that aperiodic ternary Z-complementary pairs are better than aperiodic ternary complementary ones of the same length in terms of the number of them. In the end, constructions of ternary Z-complementary sets and their mates are given.