The relative length change Delta l/l and the electrical resistivity of various alpha'-PdH x alloys with 0.66< or= x< or= 0.69 are measured simultaneously by means of a bi-dilatometer. Delta l/l increases by approximately 5* 10-5 when the samples are slowly cooled down through the 50K phase transition. Application of a constant uniaxial stress to the sample increases Delta l/l at the ordering temperature as a result of a preferential alignment of the ordered tetragonal domains along the sample axis. From the time dependence of Delta l/l one concludes that the fraction of the volume of the sample occupied by the ordered phase varies exponentially with a time constant of approximately 50 h at 47K for a PdH 0.67 alloy.