  We present one year of optical and near-infrared photometry and spectroscopy
of the Type IIP SNe 2013K and 2013am. Both objects are affected by significant
extinction, due to their location in dusty regions of their respective host
galaxies, ESO 009-10 and NGC 3623 (M65). From the photospheric to nebular
phases, these objects display spectra congruent with those of underluminous
Type IIP SNe (i.e. the archetypal SNe 1997D or 2005cs), showing low
photospheric velocities (~2 X 10**3 km/s at 50d) together with features arising
from Ba II which are particularly prominent in faint SNe IIP. The peak V-band
magnitudes of SN 2013K (-15.6 mag) and SN 2013am (-16.2 mag) are fainter than
standard-luminosity Type IIP SNe. The ejected Nickel masses are 0.012+-0.010
and 0.015+-0.006 Msol for SN 2013K and SN 2013am, respectively. The physical
properties of the progenitors at the time of explosion are derived through
hydrodynamical modelling. Fitting the bolometric curves, the expansion velocity
and the temperature evolution, we infer total ejected masses of 12 and 11.5
Msol, pre-SN radii of ~460 and ~360 Rsol, and explosion energies of 0.34 foe
and 0.40 foe for SN 2013K and SN 2013am. Late time spectra are used to estimate
the progenitor masses from the strength of nebular emission lines, which turn
out to be consistent with red supergiant progenitors of ~15 Msol. For both SNe,
a low-energy explosion of a moderate-mass red supergiant star is therefore the
favoured scenario.
