It is proved that every immersion of a compact oriented two-dimensional smooth manifold into R3 can be arbitrarily C2-approximated by smooth immersions β whose principal configurations Pβ = (Uβ ,Fβ ,fβ) defined by umbilical points and families of lines of principal curvature, are stable under C3-sufficiently small perturbations of β. Actually, the elements β are found in the class Sr, r≥4, of C3-principally structurally stable immersions, introduced in [3].