  We consider the inverse problem of determining some class of nonlinear terms
appearing in an elliptic equation from boundary measurements. More precisely,
we study the stability issue for this class of inverse problems. Under suitable
assumptions, we prove a Lipschitz and a H\"older stability estimate associated
with the determination of quasilinear and semilinear terms appearing in this
class of elliptic equations from measurements restricted to an arbitrary parts
of the boundary of the domain. Besides their mathematical interest, our
stability estimates can be useful for improving numerical reconstruction of
this class of nonlinear terms. Our approach combines the linearization
technique with applications of suitable class of singular solutions.
