  We perform an explicit two-loop calculation of the dilatation operator acting
on single trace Wilson operators built from holomorphic scalar fields and an
arbitrary number of covariant derivatives in N=2 and N=4 supersymmetric
Yang-Mills theories. We demonstrate that its eigenspectrum exhibits double
degeneracy of opposite parity eigenstates which suggests that the two-loop
dilatation operator is integrable. Moreover, the two-loop anomalous dimensions
in the two theories differ from each other by an overall normalization factor
indicating that the phenomenon is not sensitive to the presence of the
conformal symmetry. Relying on these findings, we try to uncover integrable
structures behind the two-loop dilatation operator using the method of the
Baxter Q-operator. We propose a deformed Baxter equation which exactly encodes
the spectrum of two-loop anomalous dimensions and argue that it correctly
incorporates a peculiar feature of conformal scalar operators -- the conformal
SL(2) spin of such operators is modified in higher loops by an amount
proportional to their anomalous dimension. From the point of view of spin
chains this property implies that the underlying integrable model is
``self-tuned'' -- the all-loop Hamiltonian of the spin chain depends on the
total SL(2) spin which in its turn is proportional to the Hamiltonian.
