The industrial production of melamine is carried out by the thermal decomposition of urea in two technological processes, using high or low pressure. The reaction may be accompanied by the formation of undesirable byproducts, oxoaminotriazines, and so-called polycondensates, mainly melam, melem, and melon, as well as their hydrates and adducts. Their presence leads to the deterioration of the quality of the final product and may lead to the release of troublesome deposits inside the apparatus of the product’s separation node. With the limited possibility of controlling the crystallization of the byproducts of the process, improving the technological process requires the precise determination of the composition of the separated insoluble reaction byproducts, which is the main objective of this work. This work presents the results of qualitative and quantitative analyses of the composition of deposits sampled in the technological process of melamine production. The full characterization of the deposits was performed using inductively coupled plasma optical emission spectroscopy (ICP-OES) and inductively coupled plasma mass spectrometry (ICP-MS) techniques. The elemental analysis (EA) of carbon, hydrogen, and nitrogen allowed us to obtain characteristic C/H, C/N, and H/N ratios. X-ray diffraction (XRD) and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy were also performed to confirm the obtained data. In addition, the morphology of the solid byproducts of the reaction was investigated, and the characteristics of the structures were determined using a scanning electron microscope. The elemental composition was investigated using scanning electron microscopy and the energy-dispersive X-ray spectroscopy (SEM-EDS) technique. The key finding of this research is that about 95% of the deposits are a mixture of melem and melem hydrate. The soluble part of the deposits contains melamine, urea, and oxyaminotriazines, as well as trace inorganic impurities.