Seven New Zealand earthquake sequences are studied statistically. These comprise six aftershock sequences and one earthquake swarm. The magnitude-stability law of Lomnitz does not hold. During the aftershock sequences the coefficient b, governing the frequency-magnitude relationship, is found to increase rapidly after the main shock, and then to decrease until the occurrence of the largest aftershock, when it again begins to increase. During the earthquake swarm, the coefficient b decreases logarithmically with time. This can be explained in terms of stress changes and is consistent with laboratory studies on rock deformation.