The pyrolysis–cracking of high-density polyethylene (HDPE) has been studied in two sequenced steps: (1) flash pyrolysis in a conical spouted bed reactor, and (2) catalytic cracking of the volatiles (waxes) in a fixed bed reactor containing a HZSM-5 zeolite catalyst, aiming light olefins as final products. The pyrolysis and cracking have been carried out isothermally at 500 °C, with a continuous feed of HDPE (1 g min−1) for up to 5 h (300 g of HDPE fed). We have correlated the catalytic deactivation by coke (carbonaceous deposits), in terms of amount and composition, with the profiles of gas composition along time on stream and space time. The amount and composition of coke in three axial positions of the catalytic bed have been elucidated using thermogravimetric (TG-TPO) and spectroscopic techniques (13C CP-MAS NMR, Raman, FTIR, FTIR-TPO-MS and FTIR-pyridine). Our results show that there are two pathways of coke formation: (i) initiation, during the first hour on stream and particularly in the inlet of the catalytic reactor; and (ii) steady coke formation, after the first hour on stream which is more severe in the last axial position of the catalytic reactor. The initiation step stems from the degradation of the waxes produced in the pyrolysis of HDPE and causes a dropping in the mesopore area of the catalyst. The steady coke formation step is caused by the condensation of light olefins and causes the degradation of the micropore area and the Brønsted acidity of the catalyst.