  We have carried out a search for optically visible post-AGB candidates in the
Small Magellanic Cloud (SMC). We used mid-IR observations from the Spitzer
Space Telescope to select optically visible candidates with a mid-IR excess. We
obtained low-resolution optical spectra for 801 candidates. After removing
contaminants and poor quality spectra, the final sample comprised of 63
post-AGB/RGB candidates of A - F spectral type. Using the spectra, we estimated
the stellar parameters: effective temperature, surface gravity and [Fe/H]. We
also estimated the reddening and deduced the luminosity using the stellar
parameters combined with photometry. Based on a luminosity criterion, 42 of
these 63 sources were classified as post-RGB candidates and the remaining as
post-AGB candidates. From the spectral energy distributions we found that 6 of
the 63 post-AGB/RGB candidates have a circumstellar shell suggesting that they
are single stars, while 27 of them have a surrounding disc, suggesting that
they are binaries. For the remaining candidates the nature of the circumstellar
environment was unclear. Variability is displayed by 38 post-AGB/RGB candidates
with common variability types being the Population II Cepheids (including
RV-Tauri stars) and semi-regular variables. This study has also revealed a new
s-process enriched RV Tauri star (J005107.19-734133.3). From the numbers of
post-AGB/RGB stars in the SMC, we were able to estimate evolutionary rates that
are in good agreement with the stellar evolution models with mass loss in the
post-AGB phase and re-accretion in the post-RGB phase. This study also resulted
in a new sample of 40 luminous young stellar objects (YSOs) of A - F spectral
type. Additionally, we also identified a group of 63 objects whose spectra are
dominated by emission lines and in some cases, a UV continuum. These objects
are likely to be either hot post-AGB/RGBs or luminous YSOs.
