  It is shown that the elliptic algebra ${\cal A}_{q,p}(\hat{sl}(2)_c)$ at the
critical level c=-2 has a multidimensional center containing some trace-like
operators t(z). A family of Poisson structures indexed by a non-negative
integer and containing the q-deformed Virasoro algebra is constructed on this
center. We show also that t(z) close an exchange algebra when p^m=q^{c+2} for m
integer, they commute when in addition p=q^{2k} for k integer non-zero, and
they belong to the center of ${\cal A}_{q,p}(\hat{sl}(2)_c)$ when k is odd. The
Poisson structures obtained for t(z) in these classical limits contain the
q-deformed Virasoro algebra, characterizing the structures at generic values of
p, q and m as new ${\cal W}_{q,p}(sl(2))$ algebras.
