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We design an adaptive model-based observer for state and parameter estimation in 2 × 2 semi-linear hyperbolic systems with uncertain parameters where we assume that one of the two distributed states is available through distributed sensing. The uncertainties appear in the equation for the unmeasured distributed state and may be non-linear in the unmeasured state, although linearly parameterized. The adaptive law is designed using a Lyapunov approach and expressed in terms of known signals by utilizing the specific model structure which gives rise to a general solution strategy valid for a large class of non-linear source terms. © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.