We report on luminescence, transmission and luminescence excitation measurements on indirect-gap AlxGa1-xAs in the composition range 0.42 less than or equal to x less than or equal to 0.86. The phonon coupling strength in transitions of bound excitons is investigated and found to be dependent on AlAs mole fraction and on the chemical species of the binding impurity. We find binding energy values of 35.5 +/- 5.5 meV for x = 0.42 and 50.0 +/- 5.5 meV for x = 0.86. The recombination of indirect-gap free excitons is strongly influenced by a so-called 'camel's back structure' (Delta = 349 meV, delta = 5.5 meV, xi = 0.092 for x = 0.42) within the lowest conduction band near the zone boundary X. The exciton binding energy amounts to 20 +/- 3 meV, much higher than reported recently in literature, and much higher than computable using a simple hydrogen model for the exciton. Temperature-dependent luminescence measurements-in the temperature range 4.2 K less than or equal to T less than or equal to 300 K-yielded a reliable relation for the temperature dependence of the indirect excitonic gap at an AlAs mole fraction of x = 0.42. From temperature-dependent measurements the binding energy of the sulphur donor was evaluated to be 95 +/- 9 meV in Al0.75Ga0.25As, being representative of AlAs-rich material. This value, more than twice that computable from a simple effective-mass model, has to be seen as a further strong hint at a pronounced anisotropy within the lowest conduction band at the X point of the Brillouin zone. Because the band structure data of AlAs and indirect-gap AlxGa1-xAs are very similar to those of the well known binary compound Gap, we consequently use the detailed knowledge on near-gap electronic states in this material to describe our experimental findings.