We show that in plasmonic or metamaterial slab waveguides, it is possible to generate slow non-dispersing wavepackets which undergo neither spatial diffraction nor temporal spreading with no nonlinear effects by forming a type of hybrid wavepacket between slow-light waveguide modes and diffraction-free Airy wavepackets. Three mechanisms are involved in their slowness: the slow-light feature of waveguide modes, the initial launching speed of hybrid wavepackets, and their acceleration along the time domain in a moving frame.