New process concepts in energy production and biofuel, which are much more reactive than coal, call for better controllability of the combustion in circulating fluidized bed boilers. Simplified analysis describing the dynamics of combustion in fluidized bed and circulating fluidized bed boilers is presented. Simple formulas for the estimation of the responses of the burning rate and fuel inventory to changes in fuel feeding are presented. Different changes in the fuel feed, such as an impulse, step change, linear increase and cyclic variation are considered. The dynamics of the burning with a change in the feed rate depends on the fuel reactivity and particle size. The response of a fuel mixture with a wide particle size distribution can be found by summing up the effect of different fuel components and size fractions. Methods to extract reaction parameters form dynamic tests in laboratory scale reactors are discussed. The residence time of fuel particles in the bed and the resulting char inventory in the bed decrease with increasing fuel reactivity and differences between coal and biomass is studied. The char inventory affects the stability of combustion. The effect of char inventory and oscillations in the fuel feed on the oscillation of the flue gas oxygen concentration is studied by model calculation. A trend found by earlier measurements is explained by the model.