We have studied the location of narrow-line Seyfert 1 (NLS1) galaxies and broad-line Seyfert 1 (BLS1) galaxies on the M_BH - sigma relation of non-active galaxies. We find that NLS1 galaxies as a class - as well as the BLS1 galaxies of our comparison sample - do follow the M_BH-sigma relation of non-active galaxies if we use the width of the [SII]6716,6731 emission lines as surrogate for stellar velocity dispersion, sigma_*. We also find that the width of [OIII]5007 is a good surrogate for sigma_*, but only after (a) removal of asymmetric blue wings, and, more important, after (b) excluding core [OIII] lines with strong blueshifts (i.e., excluding galaxies which have their [OIII] velocity fields dominated by radial motions, presumably outflows). The same galaxies which are extreme outliers in [OIII] still follow the M_BH - sigma relation in [SII]. We confirm previous findings that NLS1 galaxies are systematically off-set from the M_BH - sigma relation if the full [OIII] profile is used to measure sigma. We systematically investigate the influence of several parameters on the NSL1 galaxies location on the M_BH - sigma plane: [OIII]_core blueshift, L/L_Edd, intensity ratio FeII/H_beta, NLR density, and absolute magnitude. Implications for NLS1 models and for their evolution along the M_BH - sigma relation are discussed.
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