Rapid progress in passively mode-locked fibre lasers is currently driven by the recent discovery of new mode-locking mechanisms, namely, the self-similarly evolving pulse (similariton) and the all-normal-dispersion (dissipative soliton) regimes. These are fundamentally different from the previously known soliton and dispersion-managed soliton (stretched-pulse) regimes. Here, we report a fibre laser in which the mode-locked pulse evolves as a similariton in the gain segment and transforms into a regular soliton in the rest of the cavity. To our knowledge, this is the first observation of similaritons in the presence of gain, that is, amplifier similaritons, within a laser cavity. The existence of solutions in a dissipative nonlinear cavity comprising a periodic combination of two distinct nonlinear waves is novel and likely to be applicable to various other nonlinear systems. For very large filter bandwidths, our laser approaches the working regime of dispersion-managed soliton lasers; for very small anomalous-dispersion segment lengths it approaches dissipative soliton lasers. .