  Inclusive jet, dijet and trijet differential cross sections have been
measured in neutral current deep-inelastic scattering for exchanged boson
virtualities $150 < Q^2 < 15000$ GeV$^2$ with the H1 detector at HERA using an
integrated luminosity of 351 pb$^{-1}}$. The multijet cross sections are
presented as a function of $Q^2$, the transverse momentum of the jet $P_T$ (the
mean transverse momentum for dijets and trijets) and the proton's longitudinal
momentum fraction of the parton participating in the hard interaction $\xi$.
The cross sections are compared to perturbative QCD calculations at
next-to-leading order and the value of the strong coupling $\alpha_s(M_Z)$ is
determined.
