An axial flow positive displacement engine has an inlet axially spaced apart and upstream from an outlet. Inner and outer bodies have offset inner and outer axes extend from the inlet to the outlet through first, second, and third sections of a core assembly in serial downstream flow relationship. At least one of the bodies is rotatable about its axis. The inner and outer bodies have intermeshed inner and outer helical blades wound about the inner and outer axes respectively. The inner and outer helical blades extend radially outwardly and inwardly respectively. The helical blades have first, second, and third twist slopes in the first, second, and third sections respectively. The first twist slopes are less than the second twist slopes and the third twist slopes are less than the second twist slopes. A combustor section extends axially downstream through at least a portion of the second section.