Is the Universe near the state of maximal expansion?

The quadratic relation between redshift and distance obtained by Nicoll and Segal (1978) is examined, and its cosmological implications are discussed. It is found that the Nicoll and Segal relation can be consistent with relativistic cosmology if the present deceleration parameter has a high value and the Hubble constant has a low value. It is shown that if the linear law of velocities is quadratic then the distances of high redshift objects should be considerably reduced and velocities which were once considered superluminal may turn out to be less than the speed of light. It is pointed out that even if the quadratic relation is substantiated, standard relativistic cosmology still may apply.