Neural networks are able to approximate a large class of input-output maps and are also attractive due to their parallel structure which can lead to numerically inexpensive weight update laws. These properties make neural networks a viable paradigm for adaptive system identification and control, and as a consequence the use of neural networks for identification and control has become an active area of research. This paper contributes to this research thrust by developing adaptive neural identification algorithms that are able to minimize the influences of extrinsic noise on the quality of the identified model. The development relies on the use of a batch ARMarkov model, a generalization of an ARMA model whose parameters include some of the Markov parameters of the system and whose output contains the system outputs at previous sample instants. Through both theoretical analyses and simulation results, this paper demonstrates the ability of the neural network predicated on a batch ARMarkov model to improve on the noise rejection properties of identification, based on either an ARMA model or a CARMA model developed by Watanabe et al. Although the focus here is on linear system identification, the paper lays a foundation for adaptive, nonlinear identification and control.