This paper describes a method for analyzing active impedance, i. e. equivalent resistance and equivalent reactance, of a narrow-band transistor Colpitts crystal oscillator. This oscillator, employing an AT-cut resonator filter, has a very narrow-band width and an achievement of extremely low phase-noise characteristics is expected. The analysis proposed is based on an algebraic formula, which employs a nonlinear approximation for transistor gm, and a simplified circuit model. Calculated results are compared with the experimental results in the frequency characteristics of the oscillator active impedance with changing the driving signal current. Good agreement between the calculation and experimental results shows that the proposed technique is suitable for designing Colpitts crystal oscillators with resonator filters. In addition we apply this technique to the analysis of dual-mode crystal oscillators.