  We test the positivity property of the chiral perturbation theory (ChPT)
pion-pion scattering amplitudes within the Mandelstam triangle. In the one-loop
approximation, ${\cal O}(p^4)$, the positivity constrains only the coefficients
$b_3$ and $b_4$, namely one obtains that $b_4$ and the linear combination
$b_3+3 b_4$ are positive quantities. The two-loops approximation gives
inequalities involving all the six arbitrary parameters entering ChPT
amplitude, but the corrections to the one-loop approximation results are small.
ChPT amplitudes pass unexpectedly well all the positivity tests giving strong
support to the idea that ChPT is the good theory of the low energy pion-pion
scattering.
