[en] Results of calculations of all tree-level Standard Model diagrams for the reaction e⁺e^-→e⁺e^-b anti b in the energy range of LEPII and the Next e⁺e^- Linear Collider are presented. The complete matrix element was calculated by means of the software package CompHEP; phase space integration and event generation were carried out with the computer programs BASES/SPRING with additional regularizations necessary in order to handle singularities. The contributions of the dominating subsets of diagrams, the possible interference terms and their influence on the Higgs signal are studied in detail. Agreement with results of previous calculations as well as with those derived from simple analytical approximations is demonstrated. Encouraging results were obtained regarding the extraction of the Higgs signal from the overwhelming background. (orig.)