Molecules with an amide functional group resemble peptide bonds, the molecular bridges that connect amino acids, and may thus be relevant in processes that lead to the formation of life. In this study, the solid state formation of some of the smallest amides is investigated in the laboratory. To this end, CH4:HNCO ice mixtures at 20 K are irradiated with far-UV photons, where the radiation is used as a tool to produce the radicals required for the formation of the amides. Products are identified and investigated with infrared spectroscopy and temperature-programmed desorption mass spectrometry. The laboratory data show that NH ₂CHO, CH ₃NCO, NH ₂C(O)NH ₂, CH ₃ C(O)NH ₂, and CH ₃NH ₂ can simultaneously be formed. The NH ₂CO radical is found to be key in the formation of larger amides. In parallel, ALMA observations towards the low-mass protostar IRAS 16293-2422B are analysed in search of CH ₃NHCHO (N-methylformamide) and CH ₃C(O)NH ₂ (acetamide). CH ₃C(O)NH ₂ is tentatively detected towards IRAS 16293-2422B at an abundance comparable with those found towards high-mass sources. The combined laboratory and observational data indicate that NH ₂CHO and CH ₃C(O)NH ₂ are chemically linked and form in the ice mantles of interstellar dust grains. A solid-state reaction network for the formation of these amides is proposed.