An expression for the increase in wave period during long distance propagation is derived from very general assumptions. To illustrate the general nature of the solution, application is made to three different geophysical phenomena: first to the tsunami from the Aleutian earthquake of 1st April, 1946; then to the long forerunners of the swell recorded at the wave station in Pendeen, England; finally to the seismic surface waves from the Montana earthquake of 28 June, 1925 and a smaller Mexican shock in 1943. In the case of the tsunami and the swell, observations and theory are in good agreement. For the seismic surface waves the theory gives at least the right order of magnitude. Application of the theory to the period increase of swell seems furthermore to provide a simple, rational basis for locating and tracking storms at sea by means of swell observations, and may therefore be of interest in weather forecasting.