A tip turbine engine (10) provides first and second turbines (32) rotatably driven by a combustor (30) generating a high-energy gas stream. The first turbine (32) is mounted at an outer periphery of a first fan (24a) , such that the first fan is rotatably driven by the first turbine (32a) . The second turbine (32b) is mounted at an outer periphery of a second fan (24b) , and is rotatably driven by the high-energy gas stream. In one embodiment, the first turbine (32a) rotatably drives a plurality of stages of first compressor blades (54) in an axial compressor (22) in a first rotational direction, while the second turbine (32b) rotatably drives a plurality of stages of second compressor blades (52) in the axial compressor (22) in a second rotational direction opposite the first. By rotatably driving alternating stages of compressor blades in opposite directions, the efficiency of the axial compressor (22) is increased and/or the number of stages of compressor blades can be reduced. Other variations are described in additional embodiments.