An increasing number of merchants are using online platforms to promote their products; however, much is still unknown about how consumers behave in response to online promotions. This study investigates factors affecting consumers' purchase intentions and purchase behaviors during online promotions. We classify consumers into two categories, one mainly affected by the time pressure of promotion and the other primarily subject to the effect of memory decay. We then propose an analytical model to capture the market demand during an online promotion. Our analytical result indicates that there exist four types of demand patterns during online promotions, i.e., U-shape, inverted U-shape, monotonically increasing, and monotonically decreasing. We subsequently explore factors that can affect the type of demand patterns, such as the product type (nondurable and durable goods), duration of the promotion, discount level, and product category. Our empirical analyses of real-world promotion and sales data from a B2C e-commerce platform validate the analytical results. The type of demand curves depends on the characteristics of the goods and promotions. For instance, the inverted U-shape demand curve appears only for nondurable consumer goods, whereas the U-shape curve exists only for durable consumer goods. Finally, in a series of counterfactual analyses based on the proposed model, we show how revenues change during an online promotion in response to varying parameters of promotions and derive some interesting observations. These findings provide important insights to online retailers and can help them better understand their consumers and optimize their product promotion strategies.