This paper proposes a novel Neural Network Adaptive Observer (NNAO) for Nonlinear Systems with Partially and Completely Unknown Dynamics (NSPCUD), subject to variable sampled and delayed output. The method involves designing a neural network observer for partially unknown nonlinear systems with sampled and delayed outputs, using a radial basis function (RBF) neural network to approximate the system's unknown part. A new weight update algorithm is proposed, along with a closed-loop output predictor for coping with variable samples, and a closed-loop integral compensation to handle variable delay. This approach is then extended to cover completely unknown systems as well. Numerical simulations and comparisons between the proposed method and previous methods on autonomous ground vehicle models were conducted to verify the effectiveness of the proposed NNAO.