Abstract To understand the slow eastward propagation of the Madden–Julian oscillation (MJO), the authors propose a new mechanism of slow eastward propagation of an unstable disturbance [slow eastward-propagating disturbance (SED)] in the tropics assuming a simplified instability source. Two conditions are necessary over the convective region associated with the SED for this mechanism: (i) moderately negative gross moist stability (GMS) and (ii) strong stretching in the lower layer. The instability due to (i) needs to be moderate for causing a propagating convective disturbance. Under the structure of twin cyclonic vortices to the west and convection to the east, stretching of planetary vorticity associated with the convection produces cyclonic vorticity, which results in eastward propagation of the vortices. Equatorial β-plane dynamics explain the positional relation between the twin vortices and convection coherently: strong equatorial low-level westerly winds accompanying the vortices induce convergence and thus convection to the eastern side of the vortices. The SED may be considered an eastward-propagating large-scale “convective vortex” (LCV). Its dynamics is ascertained by parameter-sweep numerical experiments using a simple model with two cumulus parameterization schemes that can produce negative GMS in the convective region. This propagation mechanism is based on dynamics and thus does not relate to the instability that may be sensitive to schemes for clouds, moisture, and radiation in realistic situations. Therefore, when an LCV is generated in the tropics under any circumstance, and strong stretching occurs, the LCV necessarily propagates eastward slowly because of the dynamics of the SED. Thus, this mechanism is applicable to the MJO.