Common approaches to the fitting of additive mixed models are based on the representation of semi-structured models as mixed models. We propose an alternative approach based on boosting techniques. Boosting originates in the machine learning community where it has been developed as a technique to improve classification procedures by combining estimates with reweighted observations. In linear mixed models as well as in semi-structured mixed models the advantage of the proposed componentwise boosting technique is that it is suitable for high dimensional settings where many influence variables are present. It allows to fit models for many covariates with implicit selection of relevant variables.