The transient behavior of superfluid turbulence is studied theoretically and experimentally with the aim of understanding the disagreement between vortex-tangle theory and past measurements of free vortex-tangle decay in superfluid He4. Scaling theory is extended and large-scale simulations based on the reconnecting-vortex model are carried out. These imply that the Vinen equation should be a reasonable approximation even for rather large transients, and predict definite values for the Vinen parameters. Direct measurements of the vortex-tangle response to a sudden change in the driving velocity are seen to be in reasonable agreement with these predictions. It is found, however, that when the vortex tangle is allowed to decay farther toward zero, it eventually crosses over into a state of anomalously slow decay, which appears to be that observed in previous experiments. We argue that this regime should be interpreted in terms of a coupled-turbulence state in which random superfluid and normal-fluid motion interacts with the vortex tangle, the whole system decaying self-consistently at a rate controlled by the normal-fluid viscosity. Several additional qualitative observations which may be relevant to the question of how the vortex tangle is initiated are also reported. © 1991 The American Physical Society.