  Fermilab fixed target experiment E791 obtained a sample of $1172 \pm 61$
events of $D^+ \to \pi^- \pi^+ \pi^+$ and 848 $\pm 44$ events of $D_s^+ \to
\pi^- \pi^+ \pi^+$ decays. We find respectively $B (D^+ \to \pi^- \pi^+ \pi^+)
/ B (D^+
  \to K^- \pi^+ \pi^+) = 0.0311 \pm 0.0018 ^
  {+0.0016}_{-0.0026}$ and $B(D_s^+ \to \pi^+ \pi^- \pi^+)
  / B(D_s^+ \to \phi \pi^+) = 0.245 \pm 0.028^{+0.019}_{-0.012}$. Using a
coherent amplitude analysis to fit the Dalitz plot of the $D^+ \to \pi^- \pi^+
  \pi^+$ decay, we find strong evidence for a scalar resonance of mass
$478^{+24}_{-23}
  \pm 17 $MeV/$c^2$ and width $324^{+42}_{-40} \pm 21$
  MeV/$c^2$, compatible with what is expected for the isoscalar meson $\sigma$
>. The $D^+ \to \sigma(500)
  \pi^+$ fraction accounts for approximately half of all three-charged-pion
decays of the $D^+$ . From the Dalitz plot analysis of the $D_s^+ \to \pi^-
\pi^+ \pi^+$ decay events, we find significant contributions from the channels
$\rho^0(770)\pi^+$, $\rho^0(1450)\pi^+$,
  $f_0(980)\pi^+$, $f_2(1270)\pi^+$, and $f_0(1370)\pi^+$. We also present new
measurement of the masses and widths of the isoscalar resonances $f_0(980)$ and
$f_0(1370)$.
