  We present the scattering lengths for the $\pi K$ processes in the three
flavour Chiral Perturbation Theory (ChPT) framework at next-to-next-to-leading
order (NNLO). The calculation has been performed analytically but we only
include analytical results for the dependence on the low-energy constants
(LECs) at NNLO due to the size of the expressions. These results, together with
resonance estimates of the NNLO LECs are used to obtain constraints on the
Zweig rule suppressed LECs at NLO, $L_4^r$ and $L_6^r$. Contrary to
expectations from NLO order calculations we find them to be compatible with
zero. We do a preliminary study of combining the results from $\pi\pi$
scattering, $\pi K$ scattering and the scalar form-factors and find only a
marginal compatibility with all experimental/dispersive input data.
