We study evolution of entanglement of two two-level atoms placed inside a
multilayered microsphere. We show that due to inhomogeneity of the field modes
this entanglement essentially depends on the atomic positions (asymmetrical
entanglement) and also on the detuning between the atomic transitions and field
frequencies. The robust and complete entanglement can be achieved even in the
resonant case when the atoms have different effective coupling constants, and
it can be extended in time if the detuning is large enough. We study
analytically the lossless case and estimate numerically the effect of
dissipative processes