Summary: 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 V. Isakov [Arch. Ration. Mech. Anal. 124, No. 1, 1–12 (1993; Zbl 0804.35150)] and special singular solutions to first determine \(a(0)\) and \(c(x)\) for \(x \in \Omega\). Based on this partial result, we are then able to determine \(a(u)\) for \(u \in \mathbb R\) by an adjoint approach.