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Linear mixtures of independent random variables (the so-called sources) are sometimes referred to as under-determined mixtures (UDM) when the number of sources exceeds the dimension of the observation space. The algorithms proposed are able to identify algebraically a UDM using the second characteristic function of the observations. With only two sensors, the first algorithm only needs an SVD. With a larger number of sensors, the second algorithm executes an ALS. The joint use of statistics of different orders is possible, and an LS solution can be computed.