The aim of this paper is to examine Banach algebras of bounded Lipschitz functions from an ultrametric space IE to a complete ultrametric field IK. Considering them as a particular case of what we call C-compatible algebras we study the interactions between their maximal ideals or their multiplicative spectrum and ultrafilters on IE. We study also their Shilov boundary and topological divisors of zero. Furthermore, we give some conditions on abstract Banach IK-algebras in order to show that they are algebras of Lipschitz functions on an ultrametric space through a kind of Gelfand transform. Actually, given such an algebra A, its elements can be considered as Lipschitz functions from the set of characters on A provided with some distance λ A. If A is already the Banach algebra of all bounded Lipschitz functions on a closed subset IE of IK, then the two structures are equivalent and we can compare the original distance defined by the absolute value of IK, with λ A .