An inverted drill motor according to one or more embodiments includes an outer housing rotatable about an internal shaft member whereby rotational speed is imparted to the outer housing in response to fluid flow between the outer housing and the internal shaft member, the outer housing to connect to a drill bit and a top drive shaft portion of the internal shaft member having a top end to connect to the drill string whereby the internal shaft member and the drill string rotate at the same speed. The inverted drill motor may be for example an inverted positive displacement motor or inverted turbodrill.