Horehound seed from Wyperfeld (Wyp90 and Wyp93) had optimum germination (98%) at constant 25 C and alternating 30/15 C at 0 MPa, while seed from Swift's Creek (SC93) had optimum germination at constant 25 to 27 C (84%) or alternating 25/15 C (95%). The Generalized Additive Models showed the effects of the three covariates (temperature, temperature difference and water potential) followed a smooth and regular pattern. Germination of SC93, Wyp90 and Wyp93 seed increased (P < 0.001) by 9.1, 6.1, and 11.6% for each degree increase in temperature difference but decreased (P < 0.001) with decreases in water potential by a factor of 4.1, 4.8, and 7.1 respectively, and ceased at −1.5 MPa. At constant temperatures the odds of germination were 27, 19, and 18% smaller for water potentials of 0, −0.25 and −0.5 MPa than when alternating temperatures varied by 15 C.