E-consumer behaviour plays a vital role in e-commerce worldwide. This paper addresses the importance of delivery time, delivery fee, and delivery reception, and the influence of delivery fee and reception on e-consumers’ behaviour by analysing the following hypotheses: delivery attributes affect e-shopping behaviour, and delivery attributes affect e-consumers’ behaviour according to their sociodemographic characteristics. Data were obtained from a web-based survey with Brazilian e-consumers, and logistic regression and artificial neural network models were estimated to assess consumer behaviour. We found that delivery fee willingness to pay and privacy are affected by delivery times according to gender. Delivery fees affect the e-consumer according to gender, the habit of purchasing books and leisure products, privacy, promotions, and pricing, and influence the e-shopping decision by age, purchase of electronic products, and promotions. Delivery reception is relevant according to age, income, gender, frequency of e-shopping, privacy, and pricing. Furthermore, delivery fees influence the e-shopping decision by age, purchase of electronic products, and promotions. Finally, delivery fee, willingness-to-pay, and privacy are characteristics influenced by reception on the e-shopping decision. Further analyses would include the dynamic aspects of e-consumer behaviour and the impacts of COVID-19 in the e-consumption patterns and its effects on e-commerce deliveries.