In this paper we view the possibilities to lance a multiple (iterative) birthday attack on NTRU. Recently Wagner's algorithm for the generalized birthday problem  allowed to speed-up several combinatorial attacks. However, in the case of NTRU we can not hope to to apply Wagner's algorithm directly, as the search space does not behave nicely. In this paper we show that we can nevertheless draw profit from a multiple birthday approach. Our approach allows us to attack ees251ep6 parameter set on a computer with only 2(52) Bits of memory and about 2(9) times faster as with Odlyzko's combinatorial attack - this is an improvement factor about 2(43) in space complexity. We thus contradict the common believe, that in comparison to computational requirements, the "storage requirement is by far the larger obstacle"  to attack NTRU by combinatorial attacks. Further, our attack is about 2(7) times faster than the space-reduced variant from  employing the same amount of memory.