Gluons are massless so move at the speed of light. Gluons also are supposed to exchange gluons themselves. Wouldn't this require the gluons which are exchanged between gluons to move even faster than light?
There have been good comments to this question, which should be in an answer, because comments have a way of disappearing, so here they are:
For any two particles traveling at the speed of light, unless they're traveling in exactly the same direction, the speed required to intercept one from the other is less than c. – @probably_someone
Gluons are massless and move at the speed of light. The difference between a photon and gluon is a gluon has a charge of the QCD field, called color. As a result they strongly interact with each other as well as quarks. As a result they are scattered around in a tiny region, sometimes called the QCD bag. At high energy the coupling is reduced and the tend to behave more freely. The gluon then behaves more like a photon moving at the speed of light. Further, gluons most certainly do not move at speeds faster than light. – @Lawrence B. Crowell
And the last,
Your confusion seems to arise due to the misconception that if an object (such as a rocket) moving at the speed of light shoots something out in the direction of its motion then that something must travel faster than light. This is not true. See the relativistic velocity addition formula . @Prahar
The above hold generally in set ups where the velocities are high and special relativity has to be used to calculate numbers. I will address gluons in particular:
Gluons are defined within a mathematical model that describes elementary particle interactions, and exist in the table of particles of the standard model. .
The construction of the standard model is such, that one cannot measure a free gluon the way one can measure a free photon because of the structure of the quantum chromodynamic force, thus there is only the mathematical definition that keeps them within a confined volume generated by the QCD forces.
Gluons are always virtual, which means that the four vector describing them in the feynman diagrams is off mass shell, thus they have a variable mass under the integral which will finally give a prediction for a measurable quantity. Thus it is not meaningful to ask about the off mass shell kinematics within hadrons, which is the only place where gluons have an existence.