  We study relationship between postulation and reduction vectors of admissible
multigraded filtrations $\mathcal F= \{\mathcal F (\underline n)\}_{\underline
n\in\mathbb Z^s}$ of ideals in Cohen-Macaulay local rings of dimension at most
two. This is enabled by a suitable generalisation of the Kirby-Mehran Complex.
An analysis of its homology leads to an analogue of Huneke's Fundamental Lemma
which plays a crucial role in our investigations. We also clarify the
relationship between the Cohen-Macaulay property of the multigraded Rees
algebra of $\mathcal F$ and reduction vectors with respect to complete
reductions of $\mathcal F.$
