One illustrative example of a transistor device disclosed herein includes, among other things, a gate structure, first and second spacers positioned adjacent opposite sides of the gate structure, and a multi-layer gate cap structure positioned above the gate structure and the upper surface of the spacers. The multi-layer gate cap structure includes a first gate cap material layer positioned on an upper surface of the gate structure and on the upper surfaces of the first and second spacers, a first high-k protection layer positioned on an upper surface of the first gate cap material layer and a second gate cap material layer positioned on an upper surface of the high-k protection layer. The first and second gate cap layers comprise different materials than the first high-k protection layer.