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We show that when  k  ≠ 2, 4, 8 the Euler class of any vector bundle over Σ  k  ℝℙ  m   is zero if the rank of the bundle is not  m  +  k , provided that  m  ≠ 3 when  k  = 6. If  k  = 2, 4, 8 we show that the Euler class of any vector bundle over Σ  k  ℝℙ  m   is zero whenever the rank of the bundle is not  kr  +  k , provided that  m  ≠ 6, 7 when  k  = 2, where  r  is the largest integer such that  kr  ≤  m .

Euler classes of vector bundles over iterated suspensions of real projective spaces