We present early-time (t < +50 d) observations of SN 2019muj (=ASASSN-19tr), one of the best-observed members of the peculiar SN Iax class. Ultraviolet and optical photometric and optical and near-infrared spectroscopic follow-up started from similar to 5 d before maximum light [t(max)(B) on 58707.8 MJD] and covers the photospheric phase. The early observations allow us to estimate the physical properties of the ejecta and characterize the possible divergence from a uniform chemical abundance structure. The estimated bolometric light-curve peaks at 1.05 x 10(42) erg s(-1) and indicates that only 0.031 M-circle dot of Ni-56 was produced, making SN 2019muj a moderate luminosity object in the Iax class with peak absolute magnitude of M-V = -16.4 mag. The estimated date of explosion is t(0) = 58698.2 MJD and implies a short rise time of t(rise) = 9.6 d in B band. We fit of the spectroscopic data by synthetic spectra, calculated via the radiative transfer code TARDIS. Adopting the partially stratified abundance template based on brighter SNe Iax provides a good match with SN 2019muj. However, without earlier spectra, the need for stratification cannot be stated in most of the elements, except carbon, which is allowed to appear in the outer layers only. SN 2019muj provides a unique opportunity to link extremely low-luminosity SNe Iax to well-studied, brighter SNe Iax.

We present the photometric and spectroscopic evolution of the Type II supernova (SN II) SN 2017ivv (also known as ASASSN-17qp). Located in an extremely faint galaxy (M-r =-10.3 mag), SN 2017ivv shows an unprecedented evolution during the 2 yr of observations. At early times, the light curve shows a fast rise (similar to 6-8 d) to a peak of M-g(max) = -17.84 mag, followed by a very rapid decline of 7.94 +/- 0.48 mag per 100 d in the V band. The extensive photometric coverage at late phases shows that the radioactive tail has two slopes, one steeper than that expected from the decay of Co-56 (between 100 and 350 d), and another slower (after 450 d), probably produced by an additional energy source. From the bolometric light curve, we estimated that the amount of ejected 5(6)Ni is similar to 0.059 +/- 0.003M(circle dot). The nebular spectra of SN 2017ivv show a remarkable transformation that allows the evolution to be split into three phases: (1) H alpha strong phase (<200 d); (2) H alpha weak phase (between 200 and 350 d); and (3) H alpha broad phase (>500 d). We find that the nebular analysis favours a binary progenitor and an asymmetric explosion. Finally, comparing the nebular spectra of SN 2017ivv to models suggests a progenitor with a zero-age main-sequence mass of 15-17M(circle dot).