  The need of mathematically formulate relations between composite materials'
properties and its resonance response is growing. This is due the fast
technological advancement in micro-material manufacturing, present in chips for
instance. In this paper two theorems are presented, providing formulas of
scattering resonance of double-layered and multilayered small volumes in terms
of the coefficient of susceptibility, being high, and the geometric
characteristics. Spectroscopy measurements of the composite medium can exploit
the formula to detect its dimension and susceptibility index.
