This paper presents a unified approach forbottleneckcapacity expansion problems. In the bottleneck capacity expansion problem, BCEP, we are given a finite ground set E, a family Fof feasible subsets of E and a nonnegative real capacity ĉefor all e ∈ E. Moreover, we are given monotone increasing cost functions f e for increasing the capacity of the elements e ∈ E as well as a budget B. The task is to determine new capacities ce ≥ ĉe such that the objective function given by maxF∈F mine∈F ce is maximized under the sideconstraint that the overall expansion cost does not exceed the budget B.We introduce an algebraic model for defining the overall expansion cost and for formulating the budget constraint. This models allows to capturevarious types of budget constraints in one general model.Moreover, wediscuss solution approaches for the general bottleneck capacityexpansion problem. For an important subclass of bottleneck capacity expansion problems we propose algorithms which perform a strongly polynomial number ofsteps. In this manner we generalize and improve a recent result ofZhang et al. [15].