  Following recent work by E. Fuchs et al., we study the Brauer-Manin
obstruction for integral points on Wehler K3 surfaces of Markoff type. In
particular, we construct some families which fail the integral Hasse principle
via the Brauer-Manin obstruction with some counting results of similar nature
to those in previous works by Ghosh-Sarnak, Loughran-Mitankin,
Colliot-Th\'el\`ene-Wei-Xu. We also give some counterexamples to strong
approximation (where integral points can exist) which can be explained by the
Brauer-Manin obstruction, and study a few aspects of rational points on affine
surfaces.
