We present the results of our study of astrometric stability of 200-in Hale (Mt. Palomar) and 10-m Keck II (Mauna Kea) telescopes, both with Adaptive Optics (AO) facilities. A group of nearby visual binaries and multiples was observed in near infrared, relative separations and position angles measured. We have also checked the influence of some systematic effects (e.g. atmospherical refraction, varying plate scale factor) on result and precision of astrometric measurements. We conclude that in visual binaries astrometrical observations it is possible to achieve much better precision than 1 miliarcsecond [mas], which in many cases allows detection of the astrometrical signal produced by planetary-mass object.