The thermal time model is widely used to describe the relationship between germination and temperature. However, the model breaks the germination curve into two parts and ignores the possibility that germination rate is constant at optimal temperatures. The purposes of this study were to investigate the relationship between temperature and germination rate within the context that optimum temperature ([T.sub.o]) may be better defined as a range rather than a single point and to test for variation in minimum temperature ([T.sub.b]) and the thermal time constant of a given subpopulation g at suboptimal temperatures [[[theta].sub.1](g)] among subpopulations. Seeds of two ryegrass cultivars, perennial ryegrass (Lolium perenne L.) 'Bronsyn' and annual ryegrass (Lolium multiflorum Lam.) 'Archie', and two tall rescue cultivars (Festuca arundinacea Schreb.) 'Flecha AR542' and 'Advance' were germinated at constant temperatures ranging from 6 to 43[degrees]C at 3[degrees]C intervals and monitored for subpopulation variability from the 10th to 80th germination percentiles. Linear regression was used to estimate the parameters of the modified thermal time model at suboptimal, optimal, and supraoptimal temperatures. The tall rescue and ryegrass cultivars all exhibited an To range over which the germination rate was constant, although the magnitude of the [T.sub.o] range depended on cultivar and/or species and subpopulations. Therefore, a modified thermal time model incorporating upper limit of optimum temperature range ([T.sub.ou]) and lower limit of optimum temperature range ([T.sub.ol]) was proposed. This modified thermal time model can better predict the germination rate and temperature relationship in some circumstances.