Muon-spin-relaxation (muSR) measurements have been performed for the partially Zn-substituted electron-doped high-T_c_ superconductor Pr_0.86_LaCe_0.14_Cu_1-y_Zn_y_O_4+alpha-delta_ with y=0-0.05 and the reduced oxygen content delta=0-0.09, in order to investigate nonmagnetic Zn-impurity effects on the Cu-spin dynamics. For all the measured samples with delta=0.01-0.09, it has been found that a fast depolarization of muon spins is observed below 100 K due to the effect of Pr^3+^ moments and that the muSR time spectrum in the long-time region above 5 mu-sec increases with decreasing temperature at low temperatures below 30 K possibly due to slowing down of the Cu-spin fluctuations assisted by Pr^3+^ moments. No Zn-induced slowing down of the Cu-spin fluctuations has been observed for moderately oxygen-reduced samples with delta=0.04-0.09, which is very different from the muSR results of La_2-x_Sr_x_Cu_1-y_Zn_y_O_4_. The possible reason may be that there are no dynamical stripe correlations of spins and electrons in the electron-doped high-T_c_ cuprates or that the effect of Pr^3+^ moments on the muSR spectra is stronger than that of a small amount of Zn impurities.
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