Understanding the neural processing of natural speech processing is an important first step for designing Brain-Computer Interface (BCI) based speech enhancement and speech recognition systems. Complex neural signals like electroencephalography (EEG) are time-varying and has a non-linear relationship with continuous speech. Linear models can decode stimulus features reliably, but the correlation between the reconstructed signal and continuous EEG remain low despite attempts at optimization. In the current application, we demonstrate the utility of a Recurrent Neural Networks (RNN) model to relate various stimuli features such as the envelope, spectrogram to the continuous EEG in a cocktail party scenario. We use a Long Short-Term Memory (LSTM) neural network architecture that has self-connecting loops which help in preserving past information to predict future value. Given that predictability plays a critical role in speech comprehension, we posit that such a neural network architecture yield better results. In attended condition, for native participants, the LSTM models yield 30% and 22% mean correlation improvement and for non-native participants, 43% and 37% improvement over linear models for envelope and spectrogram respectively with EEG. Finally, we have trained a single model to predict the native language of a participant using EEG and it yielded 95% accuracy.