Patterns of change in temperature requirements for germination of achenes of four Texas winter annual Asteraceae were investigated as they afterripened at simulated summer habitat temperatures. In addition, temperature requirements for after-ripening were determined. In Gaillardia pulchella, Krigia gracilis, and Pyrrhopappus multicaulis, the maximum temperature for germination increased during afterripening (type 1 response pattern). This is the first report of a type 1 pattern in the Asteraceae. In Hymenoxys linearifolia, the maximum and minimum temperatures for germination increased and decreased, respectively, increasing to two the number of winter annuals with a type 3 response pattern. As in winter annuals in other plant families, achenes of the four species required exposure to moderately high temperatures (25:15, 30:15 °C) to gain the ability to germinate to high percentages at autumn temperatures in autumn. Of the 32 species of Asteraceae whose afterripening pattern has been investigated, 3 have type 1, 22 have type 2, and 7 have type 3. Evidence suggests that types 1 and 3 and types 2 and 3 are more closely related physiologically than are types 1 and 2. Key words: winter annuals, Asteraceae, achenes, seed germination, afterripening.