The objective of this work is to report on the influence of muon interactions on the development of air showers initiated by astroparticles. We make a comparative study of the different theoretical approaches to muon bremsstrahlung and muonic pair production interactions. A detailed algorithm that includes all the relevant characteristics of such processes has been implemented in the AIRES air shower simulation system. We have simulated ultra high energy showers in different conditions in order to measure the influence of these muonic electromagnetic interactions. We have found that during the late stages of the shower development (well beyond the shower maximum) many global observables are significantly modified in relative terms when the mentioned interactions are taken into account. This is most evident in the case of the electromagnetic component of very inclined showers. On the other hand, our simulations indicate that the studied processes do not induce significant changes either in the position of the shower maximum or the structure of the shower front surface.