The recently discovered superconductivity in MgB₂ has created the world sensation. In spite of the relatively high superconducting transition temperature T_c=39 K, the superconductivity is understood in terms of rare two gap superconductor with energy gaps attached to the \sigma and \pi -band. However, this simple model cannot describe the temperature dependent anisotropy in H_c2 or the temperature dependence of the anisotropic magnetic penetration depth. Here we propose a model with two anisotropic energy gaps with different shapes. Indeed the present model describes a number of peculiarities of MgB₂ which have been revealed only recently through single crystal MgB₂.

PACS numbers: 74.20.Rp, 74.25.Bt, 74.70.Ad