We consider the Cauchy problem for the weakly coupled parabolic system ∂t wλ-Δ wλ = F(w λ) in R N , where λ > 0, w λ = (u λ, v λ), F(w λ) = (v λp , u λq ) for some p, q ≥ 1, pq > 1, and w λ(0) = (λφ1, λ q+1/p+1φ2), for some nonnegative functions φ1, φ2 ∈ C 0(R N ). If (p, q) is sub-critical or either φ1 or φ2 has slow decay at ∞, w λ blows up for all λ > 0. Under these conditions, we study the blowup of w λ for λ small. © 2007 Birkhaeuser.