A mathematical theory of interstitial fluid motion and capillary exchange is developed in order to understand and explain measurements of capillary and interstitial fluid pressure in the bat wing, in which a high degree of vasomotor activity occurs. As a result of precapillary sphincter activity, fluid is alternately filtered and reabsorbed from the capillary, and previous studies of related steady problems by the author suggest that the interstitial fluid pressure should oscillate with time. Wiederhielm and Weston did not observe such fluctuations when they measured tissue pressures near the capillaries. This apparent paradox is resolved in the present paper by including unsteady effects. It is shown that pressure oscillations are predicted, but because of the very high vasomotor frequency they die out within a very short distance from the capillary wall. The capillary pressure measurements of Wiederhielm and Weston are also explained in terms of precapillary sphincter activity.