Let α ∈ ] 0 , 1 [. Let Ω o be a bounded open domain of R n of class C 1 , α . Let ν Ω o denote the outward unit normal to ∂ Ω o . We assume that the Steklov problem Δ u = 0 in Ω o , ∂ u ∂ ν Ω o = λ u on ∂ Ω o has a multiple eigenvalue λ ˜ of multiplicity r. Then we consider an annular domain Ω ( ϵ ) obtained by removing from Ω o a small cavity of class C 1 , α and size ϵ > 0, and we show that under appropriate assumptions each elementary symmetric function of r eigenvalues of the Steklov problem Δ u = 0 in Ω ( ϵ ), ∂ u ∂ ν Ω ( ϵ ) = λ u on ∂ Ω ( ϵ ) which converge to λ ˜ as ϵ tend to zero, equals real a analytic function defined in an open neighborhood of ( 0 , 0 ) in R 2 and computed at the point ( ϵ , δ 2 , n ϵ log ϵ ) for ϵ > 0 small enough. Here ν Ω ( ϵ ) denotes the outward unit normal to ∂ Ω ( ϵ ), and δ 2 , 2 ≡ 1 and δ 2 , n ≡ 0 if n ⩾ 3. Such a result is an extension to multiple eigenvalues of a previous result obtained for simple eigenvalues in collaboration with S. Gryshchuk.