The Vlasov kinetic approach is used to study the stability of magnetic surfaces with respect to spontaneous excitation of collisionless tearing perturbations within magnetopause current layers (MCLs) with asymmetrical magnetic field profiles. For the unperturbed configuration a ''tractable'' (that is, with a minimum number of free parameters) Vlasov equilibrium model describing a tangential discontinuity is developed. In this model, asymmetrical MCLs are not electrostatically equipotential configurations and their structure is only determined by the angle of the magnetic field rotation &thgr;0 and the magnetic field asymmetry factor &kgr;B =(B2-B1)/B2, where B1 and B2 are the magnetic field intensities in the adjacent magnetosheath and magnetospheric regions, respectively. The stochastic percolation model by Galeev et al. (1986), based on the symmetrical charge-neutral Harris equilibrium, is generalized for asymmetrical MCLs. Asymmetry in the B field profile strongly modifies the dependence of the marginal MCL thickness (below which the MCL is subjected to percolation) on the polarity of the interplanetary magnetic field (IMF). For a northward IMF (&thgr;00.3, the maximum thickness of MCLs subjected to percolation is achieved for &thgr;0>90¿, that is, for a southward IMF. Assuming that the magnetopause should, on the average, be close to its stability threshold, realistic asymmetrical MCLs (with &kgr;B>0.3) should be thinner for a northward IMF than for a southward IMF. ¿ American Geophysical Union 1995