Geosynchronous magnetopause crossing (GMC) data were collected from literature sources from 1967 to 1993 (189 GMCs) and from the experimental data on magnetic measurements on GOES (129 GMCs) and plasma measurements on LANL (197 GMCs) geosynchronous satellites in 1994 to 2001. The dawn-dusk asymmetry of the magnetopause at geosynchronous orbit was examined by two independent methods using the collected data set of 515 GMCs. First, the large amount of accumulated GMCs permitted the revealing of a substantial dawn-dusk asymmetry in the local time (LT) distribution of the GMC occurrence probability, with a statistically significant maximum in the range from 1000 LT to 1100 LT. Second, an analysis of the dawn-dusk asymmetry dependence on the upstream solar wind conditions was performed using a scatter plot of the solar wind total pressure versus local time for various IMF Bz. There was no asymmetry revealed for large positive Bz. Under strong negative Bz we found a prominent magnetopause dawn-dusk asymmetry. The asymmetry is characterized by a shifting of the GMCs with the minimal required solar wind total pressure toward the dawn and by a significantly lower (about 3 times) solar wind pressures required for the GMCs in the dawn sector relative to the dusk sector. We found that the asymmetry cannot be attributed to the IMF orientation along the Parker spiral, which is not revealed for strongly disturbed solar wind conditions accompanying the GMCs. An application of the dawn-dusk asymmetry effect for the Chao et al.  model provided a substantial increase in the model predictive capability interim of the geosynchronous magnetopause crossings. The standard deviation decreased by 20% from 0.55 RE for the initial version to 0.45 RE for the asymmetrical version of the model, with the magnetopause axis rotated by an angle of about 15° toward the dawn. The physical processes responsible for the magnetopause dawn-dusk asymmetry are discussed. We indicate the two most probable magnetospheric phenomena, which would contribute to the substantial dawn-dusk asymmetry of the magnetopause under disturbed solar wind and geomagnetic conditions. The first one is that magnetopause erosion would operate more intensively in the prenoon sector. The second phenomenon is an asymmetrical terrestrial ring current that would develop during geomagnetic storms.