  From an analysis of the ionisation energy loss of charged particles selected
from a sample of 147926 e+e- -> tau+tau- candidates recorded in the OPAL
detector at e+e- centre-of-mass energies near the Z0 resonance, we determine
the branching ratios: BR(tau- -> nu_tau K- pi- pi+ (pi0)) = 0.343 +- 0.073 +-
0.031 % BR(tau- -> nu_tau K- pi- K+ (pi0)) = 0.159 +- 0.053 +- 0.020 % where
the (pi0) notation refers to decay modes with or without an accompanying
pizero. The tau- -> nu_tau K- pi- pi+ (pi0) final states occurring through tau-
-> nu_tau K- K_s (pi0) are treated as background in this analysis. We also
examine the resonant structure of tau- -> nu_tau K- pi- pi+ candidates. Under
the assumption that the resonant structure is dominated by the K_1 resonances,
we determine the ratio of the BR (tau- -> K_1(1270)) to the sum of the BRs (tau
-> K_1(1270) and (tau -> K_1(1400)) to be 0.71 +- 0.16 +- 0.11. In all results,
the first uncertainties are statistical and the second are systematic.
