Contextual sequence mapping is one of the fundamental problems in Natural Language Processing (NLP). Here, instead of relying solely on the information presented in the text, the learning agents have access to a strong external signal given to assist the learning process. In this paper, we propose a novel family of Recurrent Neural Network unit: the Context-dependent Additive Recurrent Neural Network (CARNN) that is designed specifically to address this type of problem. The experimental results on public datasets in the dialog problem (Babi dialog Task 6 and Frame), contextual language model (Switchboard and Penn Tree Bank) and question answering (Trec QA) show that our novel CARNN-based architectures outperform previous methods.