Actually, two mayflies. That is, unless they're not mayflies.
Krzeminski, W. & C. Lombardo. 2001. New fossil Ephemeroptera and Coleoptera from the Ladinian (Middle Triassic) of Canton Ticino (Switzerland). Rivista Italiana de Paleontologia e Stratigrafia 107 (1): 69-78.
The Triassic is apparently not a fantastic time, insect-wise. Fossil insects from the Triassic are fairly few and far between. Needless to say, this is really annoying, because it was probably a fairly significant time in insect evolution. The giant insects of the Palaeozoic were no more - instead, it was about this time that many of the modern insect orders stepped in to take their place (Grimaldi & Engel, 2005). This unfortunately brief paper by Krzeminski & Lombardo (2001) gives us just a couple of pieces of the puzzle, but it's debatable just what we can do with them.
First, the maybe-mayfly. Krzeminski & Lombardo described Tintorina from two specimens (unfortunately, while the name Tintorina triassica appears in the abstract, the name used in the body of the article is Tintorina meridensis - I'm not sure, but I think the latter would be the correct name). The holotype retains most of the body (the head is missing), two of the wings and a few bits of leg. The paratype is just a pair of wings and a fragment of body. Though fragmentary, this collection does not put us too badly off. A large percentage of insect fossil species are only known from the wings, and the pattern of venation therein is hence the most commonly used suite of characters for distinguishing taxa. Krzeminski & Lombardo assign Tintorina to a new family of Ephemeroptera. They cite the wing venation and the general body shape as their reason for doing so, but unfortunately do not note exactly which features of the venation they refer to. Features such as the absence of a humeral vein (a small vein near the base of the wing) indicate that, if Tintorina is related to Ephemeroptera, it must lie outside the crown group. The only author to specifically comment on Tintorina since seems to be Kluge (2004), who concurred in the overall similarity of venation with Ephemeroptera, but also noted a couple of significant differences. As a result, Kluge moved Tintorina to Pterygota incertae sedis.
Next, the beetle. Coleoptera fossils are known since the Lower Permian, but carry problems all of their own. Almost the entire early fossil record of beetles is composed of isolated elytra, which offer few diagnostic characters and which may be suspected of rampant homoplasy (Ponomarenko, 2002). While representatives of recent families or their close relatives have been described from early on, a lot of doubt must hang over the accuracy of these identifications. A classic example is the Triassic family Obrieniidae, originally identified as the earliest representatives of the weevils (Curculionoidea), but now regarded as merely convergent (Kuschel, 2003). In the case of Krzeminski & Lombardo (2001), they assign a single elytron to the genus Notocupes in the family Cupedidae. The Cupedidae survive to this day - an example of a living species (Tenomerga mucida) is shown at the top of the post in a photo from Wikipedia. Generally found in rotten wood, the are one of the few survivors of the basal (paraphyletic?) beetle suborder Archostemata, making them very interesting in understanding beetle evolution. The genus Notocupes (recently regarded as a synonym of Zygadenia by Ponomarenko, 2006) is a fossil genus known from Triassic to the Palaeocene - a really quite spectacular length of time, and, in light of the problems I've just mentioned, really worth a further look.
Kluge, N. 2004. The Phylogenetic System of Ephemeroptera. Springer.
Kuschel, G. 2003. Nemonychidae, Belidae, Brentidae (Insecta: Coleoptera: Curculionoidea). Fauna of New Zealand 45.
Ponomarenko, A. G. 2002. Superorder Scarabaeidea Laicharting, 1781. Order Coleoptera Linné, 1758. The beetles. In History of Insects (A. P. Rasnitsyn & D. L. J. Quicke, eds.) pp. 164-176. Kluwer Academic Publishers: Dordrecht.
Ponomarenko, A. G. 2006. [On the types of Mesozoic archostematan beetles (Insecta, Coleoptera, Archostemata) in the Natural History Museum, London]. Paleontologicheskii Zhurnal 2006 (1): 86-94 (transl. Paleontological Journal 40 (1): 90-99).