Hilbert functions and Hilbert polynomials of Zs-graded admissible filtrations of ideals {F(n)}n∈Zs such that λ(R/F(n)) is finite for all n∈Zs are studied. Conditions are provided for the Hilbert function HF(n):=λ(R/F(n)) and the corresponding Hilbert polynomial PF(n) to be equal for all n∈Ns. A formula for the difference HF(n)-PF(n) in terms of local cohomology of the extended Rees algebra of F is proved which is used to obtain sufficient linear relations analogous to the ones given by Huneke and Ooishi among coefficients of PF(n) so that HF(n)=PF(n) for all n∈Ns. A theorem of Rees about joint reductions of the filtration {IrJs}r,s∈Z is generalised for admissible filtrations of ideals in two-dimensional Cohen-Macaulay local rings. Necessary and sufficient conditions are provided for the multi-Rees algebra of an admissible Z2-graded filtration F to be Cohen-Macaulay. © 2015 Elsevier Inc.