This paper tackles the problem of processing and combining efficiently arbitrary long data streams, coming from different modalities with different acquisition frequencies. Common applications can be, for instance, long-time industrial or real-life systems monitoring from multimodal heterogeneous data (sensor data, monitoring report, images, etc.). To tackle this problem, we propose StreaMulT, a Streaming Multimodal Transformer, relying on cross-modal attention and an augmented memory bank to process arbitrary long input sequences at training time and run in a streaming way at inference. StreaMulT reproduces state-of-the-art results on CMU-MOSEI dataset, while being able to deal with much longer inputs than other models such as previous Multimodal Transformer.