For pt.II see ibid., vol.15, no.2, p.219-31 (1982). The satellite structure in the argon L X-ray emission spectrum has been calculated using correlated initial- and final-state wavefunctions based upon a frozen-core model for each state developed previously. Strong correlation effects in the final state give rise to intense satellite structure similar to the photoelectron satellites seen in valence-shell ionisation. The intensities differ from the photoelectron intensities as a result of relaxation in the transition process. Final-state correlation satellites investigated in this work contribute a total intensity equal to 84% of the diagram line intensity to the spectrum. Multiply-excited correlation satellites also exist and contribute a total intensity estimated to be 6.0% of the diagram line intensity for the initial excited-state populations chosen in this study. A few initial-state correlation satellites are also predicted with this distribution contributing about 0.3% intensity to the spectrum. The theoretical predictions are compared with current experimental work. Evidence is presented that the incident energy dependence of main-line to satellite-line intensities recently reported by Bonnet et al. (1980) is not due to variations in final-state correlation satellite intensities as originally proposed by these workers. The present paper highlights the important role of electron correlation effects in determining X-ray satellite structure and provides an insight into the complexity of the calculations required.