We demonstrate the first semiconductor mode-locked lasers for ultrashort pulse generation at the 760 nm waveband. Multi-section laser diodes based on an AlGaAs multi-quantum-well structure were passively mode-locked, resulting in the generation of pulses at around 766 nm, with pulse durations down to ~4 ps, at pulse repetition rates of 19.4 GHz or 23.2 GHz (with different laser cavity lengths of 1.8 mm and 1.5 mm, respectively). The influence of the bias conditions on the mode-locking characteristics was investigated for these new lasers, revealing trends which can be ascribed to the interplay of dynamical processes in the saturable absorber and gain sections. It was also found that the front facet reflectivity played a key role in the stability of mode-locking and the occurrence of self-pulsations. These lasers hold significant promise as light sources for multi-photon biomedical imaging, as well as in other applications such as frequency conversion into the ultraviolet and radio-over-fibre communications.