The design of a Galilean-type free-fall experiment to test Einstein's Equiv
alence Principle at an improved level of sensitivity is described. Two test
bodies of different material fall down from a height of 109 m inside of an
evacuated drop tube (Drop Tower Facility Bremen, Germany). Their possible
relative displacement will be measured using LTS DC SQUID based position se
nsors, Experiences and results of this experiment meet directly the current
STEP project of NASA/ESA to test the Equivalence Principle in space at a l
evel of one part in 10(18). Several issues of the developed measuring syste
m are discussed, above all, the performance of two types of SQUID position
sensors. Furthermore some recent results of free fall tests of components o
f the measuring system at the Bremen Drop Tower are presented.