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Oscillatory plant transpiration has been observed in numerous plants, and it is now believed to be a common rather than an exceptional phenomenon. It is related directly to cyclic variations of the stomatal aperture and indirectly to the water content of guard, subsidiary and mesophyll cells. At least for small plants the upward transport of water from the roots to the leaves and the surrounding atmosphere can be explained entirely in terms of the biologically passive forces of capillarity and transpiration-cohesion. Biologically active forces involving energy consuming pumping also exist, but in small plants they play a minor rôle in the dynamics of the oscillatory water transport. On the macroscopic level of the whole plant the water transport can thus be formulated in terms of an analogue hydraulic-elastic model, by modifying somewhat that formulated in 1972 by Cowan. Differential equations corresponding to this modified model are established and conditions for the existence of periodic solutions are derived. It turns out that these conditions are not very severe mathematically. A considerable freedom is left in particular in the choice of the non-linear dependence between the stomatal aperture and the water content of guard, subsidiary and mesophyll cells. In a given plant there is of course no such freedom, because this dependence is entirely fixed by the mechanical structure of the stomatal complex. Several types of operation of the stomatal complex are possible, because mathematically there is more than one possibility to match the oscillatory waveforms to the experimentally observed ones.