We present a study of intermediate-z Type Ia supernovae (SNe Ia) using empirical physical diagrams which permit the investigation of those SNe explosions. This information can be very useful to reduce systematic uncertainties of the Hubble diagram of SNe Ia up to high z. The study of the expansion velocities and the measurement of the ratio (Si II) allow subtyping of SNe Ia as done in nearby samples. The evolution of this ratio as seen in the diagram (Si II)-(t) together with (Si II)_max versus (B – V)₀ indicates consistency of the properties at intermediate-z compared with the nearby SNe Ia. At intermediate-z, expansion velocities of Ca II and Si II are found similar to those of the nearby sample. This is found in a sample of six SNe Ia in the range 0.033 ≤z≤ 0.329 discovered within the International Time Programme of SNe Ia for Cosmology and Physics in the spring run of 2002.⁷The program run under Omega and Lambda from Supernovae and the Physics of Supernova Explosions within the International Time Programme at the telescopes of the European Northern Observatory (ENO) at La Palma (Canary Islands, Spain). Two SNe Ia at intermediate-z were of the cool FAINT type, one being an SN1986G-like object highly reddened. The (Si II) ratio as well as subclassification of the SNe Ia beyond templates help to place SNe Ia in their sequence of brightness and to distinguish between reddened and intrinsically red supernovae. This test can be done with very high z SNe Ia and it will help to reduce systematic uncertainties due to extinction by dust. It should allow to map the high-z sample into the nearby one.