  We present a sequential version of the multilinear Nystr\"om algorithm which
is suitable for the low-rank Tucker approximation of tensors given in a
streaming format. Accessing the tensor $\mathcal{A}$ exclusively through random
sketches of the original data, the algorithm effectively leverages structures
in $\mathcal{A}$, such as low-rankness, and linear combinations. We present a
deterministic analysis of the algorithm and demonstrate its superior speed and
efficiency in numerical experiments including an application in video
processing.
