Astrometric search for extrasolar planets in stellar multiple systems Taking our own solar system as an archetype most exoplanet search programs are concentrated on single and solar like stars. However it is an accepted estimation that about the half of all stars are a member of a stellar multiple systems but the multiplicity rate of the currently known exoplanet host stars is just about 17%. Furthermore differences are found comparing the properties of planets around single stars and in stellar multiple systems. The mass as well as the number of planets in such stellar multiple systems depends on the separation of its host star to the nearest stellar companion. For the closest stellar systems known today harboring at least one exoplanet that separation is about 20 AU which indicates an existing lower limit in the binary separation for stable planet formation. Astrometric imaging assisted by an adaptive optics system achieves an angular resolution down to 0.1 as which is ideal to search for planets in such close binary stars where planet formation is affected by a close stellar companion. Regarding disturbing effects like e.g. atmospheric refraction and stellar aberration an astrometric search program was developed and tested on the binary star HD19994. While trying to detect the astrometric signal of a RV planet candidate around the primary a new low mass star (0.335 solar masses) around the secondary was found by the astrometric observations (confirmed by speckle interferometry as well as follow up RV observations). Looking at the astrometric residuals any further astrometric signal larger than 1 mas can be excluded which results in an upper mass of about 12 Jupiter masses for HD 19994 Ab thus it is a planet. The final multi epoch precision achieved in this work is about 0.1 mas which is one of the highest astrometric precisions reached by ground based observations. That precision enables to detect Jovian planets around nearby solar like stars and even less mass planets around nearby low mass stars.