This thesis deals with the derivation of new semi-analytical methods for the modelling of combustion instabilities in anchored laminar flame combustors. In a first part, through an analysis of the motion of the acoustic discontinuity in a ducted flame model, it shows that the movement of the flame induced discontinuity can lead to stability changes. For unstable combustors, it can also affect the amplitude of limit cycle oscillations. In a second part, the problems that are encountered when attempting to obtain the transfer functions for linearly unstable systems from within limit cycle are demonstrated. Indeed, under these circumstances, both the phase and amplitude of the unstable mode need to be corrected. Whilst the correction to the phase can easily be determined, the correction to the gain cannot, supporting the need for robust model based controllers or adaptive control methods which do not require system identification. Lastly, this thesis presents the derivation and implementation of the first asymptotic-based mathematical models which account for the flame motion, hydrodynamic field and acoustic field in an anchored ducted flame setup. This modelling exploits the difference in length scales associated with the flame, hydrodynamic field and acoustic waves. Unlike ducted flame models which omit the hydrodynamic field, this allows us to capture instability mechanisms such as Rayleigh-Taylor, or Darrieus-Landau instabilities, in the context of anchored laminar flames. This is done for two simplified configurations: a weakly conical flame shape, and a conical flame shape case with small mean heat release.