  Let G be a reductive group over a non-archimedean local field F. Consider an
arbitrary Bernstein block Rep(G)^s in the category of complex smooth
G-representations. In earlier work the author showed that there exists an
affine Hecke algebra H(O,G) whose category of right modules is closely related
to Rep(G)^s. In many cases this is in fact an equivalence of categories, like
for Iwahori-spherical representations.
  In this paper we study the q-parameters of the affine Hecke algebras H(O,G).
We compute them in many cases, in particular for principal series
representations of quasi-split groups and for classical groups.
  Lusztig conjectured that the q-parameters are always integral powers of q_F
and that they coincide with the q-parameters coming from some Bernstein block
of unipotent representations. We reduce this conjecture to the case of simple
p-adic groups, and we prove it for most of those.
