The structural energetics of PdTi and PtTi have been studied using first-principles densityfunctional theory with pseudopotentials and a plane-wave basis. We predict that in both materials, the experimentally reported orthorhombic B19 phase will undergo a low-temperature phase transition to a monoclinic B19 ′ ground state. Within a soft-mode framework, we relate the B19 structure to the cubic B2 structure, observed at high temperature, and the B19 ′ structure to B19 via phonon modes strongly coupled to strain. In contrast to NiTi, the B19 structure is extremely close to hcp. We draw on the analogy to the bcc-hcp transition to suggest likely transition mechanisms in the present case.