Monitoring the depth of anesthesia (DOA) during surgery is very important in order to avoid patients' interoperative awareness. Since the traditional methods of assessing DOA which involve monitoring the heart rate, pupil size, sweating etc, may vary from patient to patient depending on the type of surgery and the type of drug administered, modern methods based on electroencephalogram (EEG) are preferred. EEG being a nonlinear signal, it is appropriate to use nonlinear chaotic parameters to identify the anesthetic depth levels. This paper discusses an automated detection method of anesthetic depth levels based on EEG recordings using non-linear chaotic features and neural network classifiers. Three nonlinear parameters, namely, correlation dimension (CD), Lyapunov exponent (LE) and Hurst exponent (HE) are used as features and two neural network models, namely, multi-layer perceptron network (feed forward model) and Elman network (feedback model) are used for classification. The neural network models are trained and tested with single and multiple features derived from chaotic parameters and the performances are evaluated in terms of sensitivity, specificity and overall accuracy. It is found from the experimental results that the Lyapunov exponent feature with Elman network yields an overall accuracy of 99% in detecting the anesthetic depth levels.