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Deep transfer learning techniques try to tackle the limitations of deep learning, the dependency on extensive training data and the training costs, by reusing obtained knowledge. However, the current DTL techniques suffer from either catastrophic forgetting dilemma (losing the previously obtained knowledge) or overly biased pre-trained models (harder to adapt to target data) in finetuning pre-trained models or freezing a part of the pre-trained model, respectively. Progressive learning, a sub-category of DTL, reduces the effect of the overly biased model in the case of freezing earlier layers by adding a new layer to the end of a frozen pre-trained model. Even though it has been successful in many cases, it cannot yet handle distant source and target data. We propose a new continual/progressive learning approach for deep transfer learning to tackle these limitations. To avoid both catastrophic forgetting and overly biased-model problems, we expand the pre-trained model by expanding pre-trained layers (adding new nodes to each layer) in the model instead of only adding new layers. Hence the method is named EXPANSE. Our experimental results confirm that we can tackle distant source and target data using this technique. At the same time, the final model is still valid on the source data, achieving a promising deep continual learning approach. Moreover, we offer a new way of training deep learning models inspired by the human education system. We termed this two-step training: learning basics first, then adding complexities and uncertainties. The evaluation implies that the two-step training extracts more meaningful features and a finer basin on the error surface since it can achieve better accuracy in comparison to regular training. EXPANSE (model expansion and two-step training) is a systematic continual learning approach applicable to different problems and DL models.