The long-period stacking order (LPSO) structures and stacking faults (SFs) in rapidly solidified powder metallurgy (RS P/M) $Mg_{97}Zn_1Y_2$ alloy were investigated by high resolution transmission electron microscopy (HRTEM) observations. The 18R-type LPSO structure with a stacking sequence of ACBCBCBACACACBABAB and a period of 4.86 nm was observed in the as-extruded RS P/M $Mg_{97}Zn_1Y_2$ alloy. After annealing at 773 K for 5 hr, the 18R-type LPSO structure was transformed to the 14H-type LPSO structure with a stacking sequence of ABABABACBCBCBC and a period of 3.64 nm. The 24R-type LPSO structure containing 24 atomic layers of ABABABABCACACACABCBCBCBC with period of 6.18 nm coexists with the 14H-type LPSO structure in the same grains. The LPSO structures contain intrinsic Type II SFs such as BCB/CABA and ABA/CBCB stacking sequences of a closely packed plane.