The present invention relates to a dosing valve and to a dosing device (15) for introducing a liquid medium into an exhaust-gas stream of an internal combustion engine (1) of a motor vehicle. The dosing device (15) has a pump (23) for delivering the liquid medium. The medium is injected into the exhaust-gas stream by means of a dosing valve (13) which can be controlled by way of an electromagnet (65). The dosing device (13) comprises a housing (33) with a stepped bore (34, 34.1, 34.2, 34.3, 34.4), wherein a pump sleeve (47) is guided sealingly in one portion (34.4) of the stepped bore (34). A hollow-bored piston (49) is guided sealingly in a central bore (48) of the pump sleeve (47). In a low-pressure chamber (61), an armature (69) is fastened to the piston (49), and furthermore a magnet sleeve (67) is fastened to the housing (33). A stop sleeve (75) is arranged on a side of the low-pressure chamber (61) situated opposite the magnet sleeve (67), wherein a stroke of the piston (49) is limited by the magnet sleeve (67) and/or by the stop sleeve (75).