Automatic spoken language assessment systems are becoming increasingly important to meet the demand for English second language learning. This is a challenging task due to the high error rates of, even state-of-the-art, non-native speech recognition. Consequently current systems primarily assess fluency and pronunciation. However, content assessment is essential for full automation. As a first stage it is important to judge whether the speaker responds on topic to test questions designed to elicit spontaneous speech. Standard approaches to off-topic response detection assess similarity between the response and question based on bag-of-words representations. An alternative framework based on Recurrent Neural Network Language Models (RNNLM) is proposed in this paper. The RNNLM is adapted to the topic of each test question. It learns to associate example responses to questions with points in a topic space constructed using these example responses. Classification is done by ranking the topic-conditional posterior probabilities of a response. The RNNLMs associate a broad range of responses with each topic, incorporate sequence information and scale better with additional training data, unlike standard methods. On experiments conducted on data from the Business Language Testing Service (BULATS) this approach outperforms standard approaches.