Ecological systems may exhibit complex dynamics, yet the spatial and temporal scales over which these play out make them difficult to explore experimentally. An alternative approach is to develop models based on detailed biological information about the systems and then fit them to observational data using nonlinear time-series techniques. I will give two examples of this approach, both involving systems with alternative states. The first is the dynamics of midges in Lake Myvatn, Iceland, which show fluctuations with amplitudes >105 yet with irregular period. A nonlinear time-series analysis demonstrates that these dynamics could be caused by the system having two states, a stable point and a stable cycle, with the irregular period caused by the population stochastically jumping from the domain of one state to the other. The second example is the dynamics of salvinia, an aquatic weed, and the salvinia weevil that was introduced into the billabongs of Kakadu to control the weed. Here the alternative states are two environmentally (seasonally) forced cycles, one in which salvinia is kept in check by the weevil and one in which it escapes. Understanding complex ecological dynamics may improve our management of vigorously fluctuating natural systems.