For sunspot cycles 1-20 (1755-1976), all cycles occurred in strings (two to six cycles in length) during which the period remained longer or shorter than the sample mean period. These strings have coincided with longterm trends of growth or decay in the amplitude of the cycle. In six out of six cases, the period of the cycle has switched from long to short (or the reverse) in coincidence with turning points in the long-term trend. This suggests that the solar dynamo has two modes with different mean periods. In the short-period mode, the amplitude of the cycle grows; in the long-period mode, the amplitude decays. The transition between modes has occurred at irregular intervals. A persistence of the long-period mode would eventually produce a grand minimum such as the Maunder minimum; a persistence of the short-period mode would produce a grand maximum. Unless the present interval between transitions turns out to be shorter than any previously observed interval, the present cycle (cycle 21) is part of a long-period, decaying trend and will be of longer-than-average duration (>133 months).