In this paper, the product of two independent and nonidentically distributed (i.n.i.d.) alpha-mu variates is considered. Exact reasonably simple closed-form expressions for the probability density function (pdf), the cumulative distribution function (cdf), and the moments of the resulting random variable (RV) are derived. These results find a wide range of applications in a number of fields, such as radar communications, multihop systems, multiple-input-multiple-input links, and cascaded communications in general. In particular, they are used here to describe a novel alpha-mu/alpha-mu composite multipath-shadowing fading model. Because the alpha-mu model alone comprises a substantial number of useful fading environments, its alpha-mu/alpha-mu composite version leads to a variety and an immense amount of composite fading distributions. The novel expressions for this rather flexible scenario compute instantaneously, constituting a powerful tool to characterize wireless fading channels.646 27202725