In this work, we consider the identifiability of two coefficients a(u) and c(x) in a quasilinear elliptic partial differential equation from the observation of the Dirichlet-to-Neumann map. We use a linearization procedure due to Isakov (1993 Arch. Ration. Mech. Anal. 124 1-12) and special singular solutions to first determine a(0) and c(x) for x ∈ Ω. Based on this partial result, we are then able to determine a(u) for by an adjoint approach.