In the framework of parametric methods for speech enhancement, one of them consists in combining an autore-gressive model for speech and a Kalman filter. This filtering is optimal in the H2 sense providing the initial state vector, the input and the observation vectors in the state space representation of the system are independent, white and Gaussian. However, these assumptions do not necessarily hold when processing speech. To avoid this prob-lem, we propose to use a H∞ filter to minimize the worst possible effects of the noises and system uncertainties on the estimation error. However, estimating the AR parameters, which set the spectral features of the signal to be retrieved, must be also addressed. For this reason, we propose a new method based on two interacting adaptive algorithms: each time a new observation is available, speech is estimated by using a H∞ filtering and the latest es-timated value of the AR parameters. Conversely, the AR parameters are estimated by using a Kalman filtering and the latest a posteriori speech signal estimate. A comparative study between Kalman and H∞ filtering is carried out, when the additive colored noise can be modelled by a Moving Average (MA) process.