Abstract: The different arrangements of domains of piezoelectric-piezomagnetic superlattices lead to different pro-perties. Piezoelectric-piezomagnetic superlattices with four types of domains in a unit cell (FPPS) are studied in detail in this work; the arrangements of a period are divided into 3 types, that is (+P,-P,+M,-M), (+P,-P,+P,〖JP2〗+M) and (+P,+M,-M,+M). For the FPPS with 〖JP2〗(+P,-P,+M,-M) domains, there is a frequency channel allowing one-way transmission of forward electromagnetic waves, and the relative bandwidth is about 326%. For the FPPS with (+P,－P,+P,+M),〖JP〗 the maximum group velocity index ngreaches 69 6951 in the frequency channel around 〖DD(-1.7mm〗-〖DD)〗=2374. The delay time is about 232 s when electromagnetic waves pass through the FPPS with the total length of 1 cm. For the FPPS with (+P,+M,－M,+M), the fast and slow waves can be switched when the electric field is applied to invert the polarization, and the change of group velocity index can reach 525. Thus, it is suggested that the FPPS can be applied to construct the one-way waveguide and slow wave delay devices.