  The gravitomagnetic clock effect and the Sagnac effect for circularly
rotating orbits in stationary axisymmetric spacetimes are studied from a
relative observer point of view, clarifying their relationships and the roles
played by special observer families. In particular Semer\'ak's recent
characterization of extremely accelerated observers in terms of the two-clock
clock effect is shown to be complemented by a similarly special property of the
single-clock clock effect.
