The reaction H + Br → 2 HBr proceeds by the following mechanism:
* Initiation 
: Br → 2 Br• (thermal) or Br + hν → 2 Br• (photochemical)
: each Br atom is a free radical, indicated by the symbol "•" representing an unpaired electron.
* Propagation (here a cycle of two steps)
: Br• + H → HBr + H•
: H• + Br → HBr + Br•
: the sum of these two steps corresponds to the overall reaction H + Br → 2 HBr, with catalysis by Br• which participates in the first step and is regenerated in the second step.
* Retardation (inhibition)
: H• + HBr → H + Br•
: this step is specific to this example, and corresponds to the first propagation step in reverse.
* Termination 2 Br• → Br
: recombination of two radicals, corresponding in this example to initiation in reverse.
As can be explained using the steady-state approximation, the thermal  reaction has an initial rate of fractional order (3/2), and a complete rate equation with a two-term denominator (mixed-order kinetics).