|In a forthcoming paper, Gross, Reeder, and Yu study a certain class of supercuspidal representations of general tamely-ramified p-adic groups, which exhibit minimal wild ramification. These so called epipelagic representations are closely related to Vinberg's invariant theory of graded Lie-algebras. In this talk we will report on work in progress to construct the L-packets corresponding to these representations and to prove their stability and endoscopic transfer. While the construction has common features with earlier constructions of tamely-ramified L-packets, some new phenomena occur. Most notably, the arithmetic information encoded in the Langlands parameter enters into the construction and leads to objects similar to the rectifying characters in the work of Bushnell and Henniart.