We consider multisource non-coherent network coding, where multiple sources send information to one or multiple receivers. We prove that this is equivalent to a ldquosubspacerdquo channel, that takes subspaces as inputs and outputs. We then show that the rate of each individual receiver is upper bounded as deltai(T - delta1 - delta2), where deltai is what we define to be the ldquodominatingrdquo dimension in the subspace codebook of source i, and T is the ldquocoherencerdquo time of the network.