The results of two sets of transverse energy measurements, performed with incident proton beams of 200 and 450 GeV/c momentum on several nuclear targets, are presented. The transverse energy cross sections dσ/d ET are measured in a pseudorapidity range including the target fragmentation region (-0.1<η<2.9) for both data sets and also in a nearly complete pseudorapidity coverage (-0.1<η<5.5) for the data taken at 200 GeV/c incident momentum. A comparison is made of the transverse energy distributions in the target fragmentation region and in the full η region. We find that the mean value of pseudorapidity of the d ET/dη distributions shifts towards the target fragmentation region as the atomic mass number of the target increases or a selection of high transverse energy events is made. A parametrization based on a simple geometrical nucleonnucleon scattering approach was found to be inadequate to describe all features of the transverse energy distributions. Finally, the VENUS model is compared with the experimental data.