Technically, they're called "basal dinosauromorphs" (but one scientist calls them "dinosaur wannabes") and I'm gonna call them dino-neanderthals.
Because it turns out that, for quite a while, dinosaurs coexisted with their more-primitive precursors, ancestors and genetic cousins--much as early humans coexisted with the similar but genetically distinct neanderthals (indeed, early humans and early neanderthals may have coexisted in a manner unsafe for discussion on a Web site that doesn't have an age-checking filter).
It had been thought that when dinosaurs arrived on the scene, they quickly out-competed--ran faster, ate more, bred more, etc--than these dinosaur wannabes. But a study mostly led by Berkeley folks suggests that these two types of ancient reptiles coexisted for as much as 20 million years.
For the record, the wannabes weren't direct evolutionary ancestors; more like descendants of a common ancestor (which I guess makes them more like dino-chimps?).
So what did these dino-neanderthal wannabes look like? One was a 15-foot-long, four-legged vegetarian with a "beaked snout." Scientists found a few other types of wannabes, "as well as remains of an apparent close relative of the well-known Triassic dinosaur carnivore Coelophysis." For all you well-knowing Coelophysis fans out there.