A speaking valve assembly (2, 200) for fitting to the machine end (13) of a tracheostomy tube (1) has a one-way valve (23, 236) that allows inhalation but prevents exhalation. The assembly further includes a pressure relief arrangement that remains closed during normal respiration and vocalisation but opens when pressure in the assembly rises above a normal level. In one arrangement the pressure relief arrangement takes the form of a ball valve (30) with a ball (32) that is lifted away from an opening (31) by excess pressure but falls back to block the opening when pressure reduces. An alternative pressure arrangement has a slidable collar (226) that normally covers vent apertures (223) in a housing (220) of the assembly. When pressure in the assembly rises above a normal level the collar (226) is pushed out to expose the vent apertures (223) and allow air to escape.