Abstract: A new definition for LP modes is introduced. The orthogonality of the LP-modes in sense of power is discussed. Based on these, a set of coupled-LP-mode equations are derived. It is found that the coupling among the LP-modes consists of two parts:1. The residual coupling resulted from variation of dielectric across the cross-section and anisotropy of the reference fiber; 2. The intrinsic coupling due to the difference between the practical and the reference fibers. Then the coupled-LP-mode equations are transformed into the coupled-ideal-mode equations. With the transformations, it is easy to express the ideal modes (i. e. eigen modes of the reference fiber) in terms of LP modes or vice versa. Thus the errors arising from simply replacing the ideal modes by the corresponding LP modes are studied and the conditions in which the replacement is permissible are obtained.