Speech is a desirable communication method between humans and computers. The major concerns of the automatic speech recognition (ASR) are determining a set of classification features and finding a suitable recognition model for these features. Hidden Markov Models (HMMs) have been demonstrated to be powerful models for representing time varying signals. Artificial Neural Networks (ANNs) have also been widely used for representing time varying quasi-stationary signals. Arabic is one of the oldest living languages and one of the oldest Semitic languages in the world, it is also the fifth most generally used language and is the mother tongue for roughly 200 million people. Arabic speech recognition has been a fertile area of reasearch over the previous two decades, as attested by the various papers that have been published on this subject.\ud This thesis investigates phoneme and acoustic models based on Deep Neural Networks (DNN) and Deep Echo State Networks for multi-dialect Arabic Speech Recognition. Moreover, the TIMIT corpus with a wide variety of American dialects is also aimed to evaluate the proposed models.\ud The availability of speech data that is time-aligned and labelled at phonemic level is a fundamental requirement for building speech recognition systems. A developed Arabic phoneme database (APD) was manually timed and phonetically labelled. This dataset was constructed from the King Abdul-Aziz Arabic Phonetics Database (KAPD) database for Saudi Arabia dialect and the Centre for Spoken Language Understanding (CSLU2002) database for different Arabic dialects. This dataset covers 8148 Arabic phonemes. In addition, a corpus of 120 speakers (13 hours of Arabic speech) randomly selected from the Levantine Arabic\ud dialect database that is used for training and 24 speakers (2.4 hours) for testing are revised and transcription errors were manually corrected. The selected dataset is labelled automatically using the HTK Hidden Markov Model toolkit. TIMIT corpus is also used for phone recognition and acoustic modelling task. We used 462 speakers (3.14 hours) for training and 24 speakers (0.81 hours) for testing. For Automatic Speech Recognition (ASR), a Deep Neural Network (DNN) is used to evaluate its adoption in developing a framewise phoneme recognition and an acoustic modelling system for Arabic speech recognition. Restricted Boltzmann Machines (RBMs) DNN models have not been explored for any Arabic corpora previously. This allows us to claim priority for adopting this RBM DNN model for the Levantine Arabic acoustic models. A post-processing enhancement was also applied to the DNN acoustic model outputs in order to improve the recognition accuracy and to obtain the accuracy at a phoneme level instead of the frame level. This post process has significantly improved the recognition performance. An Echo State Network (ESN) is developed and evaluated for Arabic phoneme recognition with different learning algorithms. This investigated the use of the conventional ESN trained with supervised and forced learning algorithms. A novel combined supervised/forced supervised learning algorithm (unsupervised adaptation) was developed and tested on the proposed optimised Arabic phoneme recognition datasets. This new model is evaluated on the Levantine dataset and empirically compared with the results obtained from the baseline Deep Neural Networks (DNNs). A significant improvement on the recognition performance was achieved when the ESN model was implemented compared to the baseline RBM DNN model’s result. The results show that the ESN model has a better ability for recognizing phonemes sequences than the DNN model for a small vocabulary size dataset. The adoption of the ESNs model for acoustic modeling is seen to be more valid than the adoption of the DNNs model for acoustic modeling speech recognition, as ESNs are recurrent models and expected to support sequence models better than the RBM DNN models even with the contextual input window. The TIMIT corpus is also used to investigate deep learning for framewise phoneme classification and acoustic modelling using Deep Neural Networks (DNNs) and Echo State Networks (ESNs) to allow us to make a direct and valid comparison between the proposed systems investigated in this thesis and the published works in equivalent projects based on framewise phoneme recognition used the TIMIT corpus. Our main finding on this corpus is that ESN network outperform time-windowed RBM DNN ones. However, our developed system ESN-based shows 10% lower performance when it was compared to the other systems recently reported in the literature that used the same corpus. This due to the hardware availability and not applying speaker and noise adaption that can improve the results in this thesis as our aim is to investigate the proposed models for speech recognition and to make a direct comparison between these models.