An analytical model is presented which describes the quasi-linear evolution of both ultralow-frequency (ULF) magnetic fluctuations and cometary ion flux in the solar wind due to continuous ion pickup. The derived solution yields both the initial exponential growth of the total wave intensity and the time-asymptotic growth proportional to time obtained in numerical simulations using a one-dimensional hybrid code with a constant rate of cometary ion injection (Gary et al., 1988, 1989). For pickup rates appropriate to cometary environment, the derived fluctuation intensity and pickup ion flux are in general accord with ULF wave observations and water group ion pitch angle distributions upstream of the bow waves at both comet Giacobini-Zinner and comet Halley. ¿American Geophysical Union 1991