In this paper, n-photon correlated-spontaneous-emission lasers (CEL's) are studied via the quantum theory of Scully-Lamb. It is shown that inversionless lasing can be exhibited; and phase squeezing can be produced in the inversionless region when the laser intensity is smaller than a certain value. The unified approach to n-photon CEL's is given and the properties between n-photon CEL's (n greater than ...