  The internal energy of high-density hydrogen plasmas in the temperature range
$T = 10,000 ... 50,000 K$ is calculated by two different analytical
approximation schemes (method of effective ion-ion interaction potential - EIIP
and Pad\'e approach within the chemical picture - PACH) and compared with path
integral Monte Carlo results. Reasonable agreement between the results obtained
from the three independent calculations is found, the reasons for still
existing differences is investigated. Interesting high density phenomena such
as the formation of clusters and the onset of crystallization are discussed.
