We study the spatially resolved stellar kinematics of two star-forming galaxies at z ~ 0.1 from the larger DYnamics of Newly Assembled Massive Objects (DYNAMO) sample. These galaxies, which have been characterized by high levels of star formation and large ionized-gas velocity dispersions, are considered possible analogues to high-redshift clumpy discs. They were observed using the Gemini Multi-Object Spectrograph instrument in integral field spectroscopy (IFS) mode at the Gemini Observatory with high spectral resolution (R ≃ 5400, equivalent to σ ≃ 24 km s-1 at the observed wavelengths) and ~6 h exposure times in order to measure the resolved stellar kinematics via absorption lines. We also obtain higher quality emission-line kinematics than previous observations. The spatial resolution (1.2 kpc) is sufficient to show that the ionized gas in these galaxies (as traced by Hα emission) is morphologically irregular, forming multiple giant clumps while stellar continuum light is smooth and well described by an exponential profile. Clumpy gas morphologies observed in IFS data are confirmed by complementary narrow-band Hα imaging from the Hubble Space Telescope. Morphological differences between the stars and ionized gas are not reflected dynamically as stellar kinematics are found to be closely coupled to the kinematics of the ionized gas: both components are smoothly rotating with large velocity dispersions (~40 km s-1) suggesting that the high gas dispersions are not primarily driven by star formation feedback. In addition, the stellar population ages of these galaxies are estimated to be quite young (60-500 Myr). The large velocity dispersions measured for these young stars suggest that we are seeing the formation of thick discs and/or stellar bulges in support of recent models which produce these from clumpy galaxies at high redshift. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.