Based on quadriphase perfect sequences and their cyclical shift versions, three families of almost perfect 16-QAM sequences are presented. When one of two time shifts chosen equals half a period of quadriphase sequence employed and another is zero, two of the proposed three sequence families possess the property that their out-of-phase autocorrelation function values vanish except one. At the same time, to the other time shifts, the nontrivial autocorrelation function values in three families are zero except two or four. In addition, two classes of periodic complementary sequence (PCS) pairs over the 16-QAM constellation, whose autocorrelation is similar to the one of conventional PCS pairs, are constructed as well.