This paper addresses the problem of limit-cycle taming,which is defined in this paper as the use ofnonlinear control laws to ensure that thelimit-cycle behaviour of the system beyond thestability boundary is of a benign rather than adestructive nature. Specifically, we consider aone-parameter (denoted by λ) autonomous dynamicsystem having algebraic nonlinearities. We assumethat the system has a stable solution, x = 0, for λ< λ0, and experiences a Hopfbifurcation at λ = λ0. Using a singularperturbation analysis about the stability boundary,it is shown that, using a simple nonlinear controllaw, limit-cycle taming is always possible in theneighbourhood of a Hopf bifurcation. The controlsystem proposed for limit-cycle taming is fullynonlinear, and therefore does not affect the linearbehaviour of the system (in particular its stabilitycharacteristics). Hence, limit-cycle taming may beused in conjunction with a standard linear activecontrol (e.g. use of linear active control toincrease the stability boundary). Applications ofthe theory to the problem of flutter arepresented.