Recurrent neural networks (RNNs) are widely used as a memory model for sequence-related problems. Many variants of RNN have been proposed to solve the gradient problems of training RNNs and process long sequences. Although some classical models have been proposed, capturing long-term dependence while responding to short-term changes remains a challenge. To this problem, we propose a new model named Dual Recurrent Neural Networks (DuRNN). The DuRNN consists of two parts to learn the short-term dependence and progressively learn the long-term dependence. The first part is a recurrent neural network with constrained full recurrent connections to deal with short-term dependence in sequence and generate short-term memory. Another part is a recurrent neural network with independent recurrent connections which helps to learn long-term dependence and generate long-term memory. A selection mechanism is added between two parts to help the needed long-term information transfer to the independent neurons. Multiple modules can be stacked to form a multi-layer model for better performance. Our contributions are: 1) a new recurrent model developed based on the divide-and-conquer strategy to learn long and short-term dependence separately, and 2) a selection mechanism to enhance the separating and learning of different temporal scales of dependence. Both theoretical analysis and extensive experiments are conducted to validate the performance of our model, and we also conduct simple visualization experiments and ablation analyses for the model interpretability. Experimental results indicate that the proposed DuRNN model can handle not only very long sequences (over 5000 time steps), but also short sequences very well. Compared with many state-of-the-art RNN models, our model has demonstrated efficient and better performance.