Pomeau-Manneville intermittency in nonstationary systems is investigated. If one of the parameters characterizing a dynamical system is changed periodically, periodic orbits may appear even when the value of this parameter remains in a range which, in the stationary case, yields chaotic behavior. This property may be used for the control of systems exhibiting intermittency. If the parameter change is not large enough, a periodic orbit does not appear but the distribution of the laminar phases is modified. In the case of type I intermittency, this means a broadening of such a distribution or, alternatively, a splitting of its right peak. We present a theory of these phenomena. Numerical simulations both for one-dimensional maps and for flows support our predictions. Some of the phenomena discussed here were observed earlier in time series of heart rate variability.