Let N1 (respectively N2) be a normal closure of a set R1 = {ui} (respectively R2 = {vj}) of cyclically reduced words of the free group F(A). In the paper we consider geometric conditions on R1 and R2 for N1 ∩ N2 = [N1,N2]. In particular, it turns out that if a presentation < A | R1,R2 > is aspherical (for example, it satisfies small cancellation conditions C(p)&T(q) with 1/p + 1/q = 1/2), then the equality N1 ∩ N2 = [N1,N2] holds.