In fractional order reactions, the order is a non-integer, which often indicates a  chemical chain reaction or other complex reaction mechanism. For example, the pyrolysis of acetaldehyde () into methane and carbon monoxide proceeds with an order of 1.5 with respect to acetaldehyde:  The decomposition of phosgene () to carbon monoxide and chlorine has order 1 with respect to phosgene itself and order 0.5 with respect to chlorine: 
The order of a chain reaction can be rationalized using the steady state approximation for the concentration of reactive intermediates such as free radicals. For the pyrolysis of acetaldehyde, the Rice-Herzfeld mechanism  is
;Initiation   :
;Propagation  :
;Termination  :
where • denotes a free radical. To simplify the theory, the reactions of the  to form a second  are ignored.
In the steady state, the rates of formation and destruction of methyl radicals are equal, so that
so that the concentration of methyl radical satisfies
The reaction rate equals the rate of the propagation steps which form the main reaction products  and CO:
in agreement with the experimental order of 3/2.