Background subtraction is an important task for visual surveillance systems. However, this task becomes more complex when the data size grows since the real-world scenario requires larger data to be processed in a more efficient way, and in some cases, in a continuous manner. Until now, most of background subtraction algorithms were designed for mono or trichromatic cameras within the visible spectrum or near infrared part. Recent advances in multispec-tral imaging technologies give the possibility to record mul-tispectral videos for video surveillance applications. Due to the specific nature of these data, many of the bands within multispectral images are often strongly correlated. In addition , processing multispectral images with hundreds of bands can be computationally burdensome. In order to address these major difficulties of multispectral imaging for video surveillance, this paper propose an online stochastic framework for tensor decomposition of multispectral video sequences (OSTD). First, the experimental evaluations on synthetic generated data show the robustness of the OSTD with other state of the art approaches then, we apply the same idea on seven multispectral video bands to show that only RGB features are not sufficient to tackle color saturation , illumination variations and shadows problem, but the addition of six visible spectral bands together with one near infra-red spectra provides a better background/foreground separation.