This paper discusses the parameter and differentiation order identification of continuous fractional order KiBaM models in ARX (autoregressive model with exogenous inputs) and OE (output error model) forms.The least squares method is applied to the identification of nonlinear and linear parameters,in which the Griinwald-Letnikov definition and short memory principle are applied to compute the fractional order derivatives.An adaptive P-type order leing law is proposed to estimate the differentiation order iteratively and accurately.Particularly,a unique estimation result and a fast convergence speed can be arrived by using the small gain strategy,which is unidirectional and has certain advantages than some state-of-art methods.The proposed strategy can be successfully applied to the nonlinear systems with quasi-linear characteristics.The numerical simulations are shown to validate the concepts.