How Do Intermodulation Products Manifest in Transmitting Equipment?
There are essentially two mechanisms: 


Internal nonlinearities, arising from non-ideal behaviour of mixers and amplifiers. 


When passed through a nonlinear device, a modulating signal containing F_1 &amp; F_2 can produce an output signal with side bands located at: 
$$\{F_1, F_2,\\ (F_1+F_2), (F_1-F_2),\\ 2*F_1, 2*F_2,\\ 2*F_1+F_2, 2*F_2+F_1,\\ 2*F_1-F_2, 2*F_2-F_1,\\ 3*F_1, 3*F_2\\ ...\}$$
Even though we want mixers that are multipliers they're often closer to Taylor series, and only approach being multipliers for a given signal domain. We also want linear amplifiers, but we also want them to be efficient and cheap... that is a tricky, tricky mix. 


Effects due to externally applied RF. 


Power amplifiers are sensitive to energy applied to the output and particularly when operated close to or in saturation, they can look an awful lot like a switching mixer if you squint just right, so again you can get sum and difference series produced. This is an especially good party trick on a shared mast with multiple co-located services where adding a transmitter can cause one that YOU do NOT own, to interfere with another receiver that you ALSO do not own... That can get amusingly political. I have had LOTS of fun with this when co-locating low band VHF kit.


  Power amplifiers are sensitive to energy applied to the output. 


To expand on this detail (from discussion in comments): It all boils down to the non-linear curve that describes the input-output relationship of an amplifier. When a voltage is introduced at the output, you're modifying that relationship. Thus, the resulting inter-modulation products observed at the output contain the sum &amp; difference of every multiple of the frequencies introduced at either the input or output.