  We study chiral operators in four-dimensional N=2 supersymmetric gauge
theories. We provide a general procedure to derive the exact relations among
the vacuum expectation values of chiral operators in the Omega-background using
the non-perturbative Dyson-Schwinger equations of qq-characters. We demonstrate
our procedure using several examples. For pure SU(N) gauge theory and SU(N)
gauge theory with 2N fundamental hypermultiplets, we verify the relations
conjectured previously in the literature. We also briefly discuss the relations
in SU(N) linear superconformal quiver gauge theories.
