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We propose an adaptive output-feedback control design technique for a class of feedforward systems with input-to-state stable (ISS) appended dynamics. The system contains uncertain functions involving all states with the assumed bounds on uncertain functions allowed to contain crossproducts of unknown parameters and unmeasured states. The ISS appended dynamics are coupled with all the system states and the input and the ISS Lyapunov inequalities also feature crossproducts of unknown parameters and unmeasured states. The proposed control design does not require any knowledge of magnitude bounds on unknown parameters.