对一类光子消灭算符aN的正交归一本征态的迭加态的振幅k次方压缩特性进行研究，结果表明一类aN的正交归一本征态的迭加态的振幅k次方压缩特性明显地区别于aN的正交归一本征态k次方压缩。无论N取奇数还是偶数迭加态均存在振幅k(k=Nt或Nt/2)次方压缩，当位相差δ=2mπ/t(m为整数)时迭加态不存在振幅k次方压缩；当δ=π时，只有N和t同时为奇数才有可能存在k次方压缩；当δ=π/2时，对应t≠4m的不同取值迭加态存在k次方压缩；因而参量的位相对振幅的k次方压缩起着关键性的作用。

The characteristics of the k th-power squeezing of a class of superposition states which involving two orthonormalized eigenstates of photon annihilation operator aN are studied. The result show that the characteristics of the k th-power squeezing of a class of superposition states which involving two orthonormalized eigenstates of photon annihilation operator aN are different from the characteristics of the k th-power squeezing of the orthonormalized eigenstates of photon annihilation operator aN clearly. No matter what N is an odd number or even number, the superposition states own amplitude k(k=Nt or Nt/2) th-power squeezing, but for the orthonormalized eigenstates of aN, only when N is even number there exist amplitude k(k=(2P+1)N/2) th-power squeezing. Owing to that, when phase difference δ=2mπ/t (m is integer), the superposition states don′t own amplitude k th-power squeezing; when δ=π, only N and t are odd number simultaneously, the superposition states may own amplitude k th-power squeezing; when δ=π/2, t≠4m, the superposition states own amplitude k th-power squeezing; thus the phase difference of parameter has key effect on amplitude k th-power squeezing.