This paper presents an L1 adaptive output feedback controller for a class of uncertain nonlinear systems in the presence of time and output dependent unknown nonlinearities. As compared to earlier introduced L 1 adaptive output feedback control architectures, the architecture in this paper relies on system inversion, and is therefore limited to minimum phase systems. Similar to prior solutions in L1 adaptive control theory, the feedback structure is comprised of the three main elements, involving predictor, adaptation laws and low-pass filter, with the only difference that the predictor here is an input predictor and not a state predictor. Whereas in prior architectures of L1 adaptive output feedback control the verification of the sufficient condition for stability, written in terms of L1 norm of cascaded systems, was not straightforward, the solution proposed in this paper, under mild assumptions on system dynamics, provides a complete parametrization of the low-pass filters for the design purposes. The closed-loop system achieves arbitrarily close tracking of the input and the output signals of the reference system. Simulations verify the theoretical findings.