A conditional parametric ARX-model is an ARX-model in which the parameters re replaced by smooth functions of an, possibly multivariate, externalinput signal. These functions are called coefficient functions is suggested. Essentially, in its most simple form, this method is a combination of recursive least squares with exponential forgetting and local polynomial regression. However, it is argued, that it is appropriate to let the forgetting factor vary with the value of the external signal shich is argument of the coeffieient-functions.The properties of the modified method are sutdied by simulation. A particular feature is that this effectiv forgetting factor will adapt to the bandwidth used so that the effective number of observtions behind the estimates will be almost independent of the actual bandwidth or of the type of bandwidth selection used (fixed or nearest neighbour). The choice of optimal bandwidth and forgetting is briefly discussed. Furthermore, a method for adaptive nd recursive estimation in additive or varying-coefficient models is suggested. This method is a semi-parametric equivalent to the recursive prediction error method.