  We examine the issue of the cosmological constant in the $many$ $inflating$
branes scenario, extending on two recent models by I.Oda and Randall-Sundrum.
The exact solution in a closed form is found in the slow roll approximation of
the radion. Defining an effective expansion rate, which depends on the location
of each brane in the fifth dimension and demanding stability for this case we
show that each positive tension brane has a localized, decaying cosmological
constant (the opposite process applies to the negative energy branes [4]) . The
reason is that the square of the effective expansion rate enters as a source
term in the Einstein equations for the branes.Thus the brane has two scale
factors depending on time and the fifth dimnesion respectively .The brane will
roll along the fifth dimension in order to readjust its effective expansion
rate in such a way that it compensates for its internal energy changes due to
inflation and possible phase transitions.
