  Deep-inelastic ep scattering data taken with the H1 detector at HERA and
corresponding to an integrated luminosity of 106 pb^{-1} are used to study the
differential distributions of event shape variables. These include thrust, jet
broadening, jet mass and the C-parameter. The four-momentum transfer Q is taken
to be the relevant energy scale and ranges between 14 GeV and 200 GeV. The
event shape distributions are compared with perturbative QCD predictions, which
include resummed contributions and analytical power law corrections, the latter
accounting for non-perturbative hadronisation effects. The data clearly exhibit
the running of the strong coupling alpha_s(Q) and are consistent with a
universal power correction parameter alpha_0 for all event shape variables. A
combined QCD fit using all event shape variables yields alpha_s(mZ) = 0.1198
\pm 0.0013 ^{+0.0056}_{-0.0043} and alpha_0 = 0.476 \pm 0.008 ^{+0.018}
_{-0.059}.
