This paper studies the following online replacement problem. There is a real function f(t), called the flow rate, defined over a finite time horizon [0; T ]. It is known that m f(t) M for some reals 0 m ! M . At time 0 an online player starts to pay money at the rate f(0). At each time 0 ! t T the player may changeover and continue paying money at the rate f(t). The complication is that each such changeover incurs some fixed penalty. The player is called online as at each time t the player knows f only over the time interval [0; t]. The goal of the player is to minimize the total cost comprised of cumulative payment flow plus changeover costs. This formulation of the replacement problem has various interesting applications among which are: equipment replacement, supplier replacement, the menu cost problem and mortgage refinancing.