The conventional oedometer uses a consolidation ring of 1.9 cm in height to hold a soil specimen. During the oedometer test only the vertical compression of the specimen is measured. This is insufficient for studying the consolidation behavior of soils. In order to study the time dependent compressibility behavior of clays during the primary consolidation, a special consolidation apparatus is built where oedometers are connected in series so that the thickness of the specimens are added up. Samples of two soils are used in the test program to measure both the vertical compression and the excess pore water pressure of the specimens. The obtained data are then used to evaluate the values of the consolidation parameters de/dt, dσ/ dt, (The equation is abbreviated).The results of analyses on the values of the consolidation parameters show that clay posses creep behavior during primary consolidation and the creep rate is not a constant. The constitutive equation of one-dimensional consolidation in previous study is verified with the sedata. The oedometers connected in series can be used to measure consolidation condition within the soil specimen during primary consolidation. Therefore, it is a valuable research apparatus in studying the consolidation behavior of clays.