The classical case of the convolution pair ( S $^{∗}$, O ∗ $_{C}$) is examined in Schwartz (1966). If ( g, f ) belong to ( S $^{∗}$, O ∗ $_{C}$) the convolution exists and equation (2) transforms into the multiplicative equation γφ = ε, where γ ∈ S $^{∗}$, φ ∈ O$_{M}$ and ε ∈ S ∗ (Schwartz, 1966, p.281-282). The product between a generalized function in S ∗ and a function from O$_{M}$ always exists in S $^{∗}$; multiplication is a hypocontinuous operation (Schwartz, 1966, p.243-246). Thus there is a dichotomous relation between the classical convolution pair ( S $^{∗}$, O ∗ $_{C}$) and the product pair of generalized functions spaces, ( S $^{∗}$, O$_{M}$ ) . Below we show that this dichotomy extends to other convolution pairs of spaces. Define a product pair of spaces as a pair ( Γ , Φ ) of subspaces of S $^{∗}$such that for any γ ∈ Γ , φ ∈ Φ the product γφ defines an element ε in S $^{∗}$; the operation of multiplication for ( Γ , Φ ) is hypocontinuous in the topology of S $^{∗}$. Theorem 1 If Assumptions 1 and 2 are satisfied then for any ( g, f ) ∈ ( A, B ) the exchange formula applies. Proof. Consider the special sequences studied by Mikusinski (Antosik et al, 1973) and Hirata and Ogata (1958) that are defined for a generalized function b as ˜ b$_{n}$ = b ∗ δ$_{n}$ with δ$_{n}$ representing the following delta-convergent sequence: for a number sequence: α$_{n}$ > 0 and α$_{n}$ → 0 , the regular function δ$_{n}$ ( x ) is non-negative with support in | x | < α$_{n}$ and ∫ δ$_{n}$ ( x ) dx = 1; the convolution with δ$_{n}$ ∈ E ∗ is always defined. Moreover, ˜ b$_{n}$ → b in S ∗ : indeed, ( b ∗ δ$_{n}$, ψ ) = ( b, ψ ∗ δ$_{n}$ ) , but ψ ∗ δ$_{n}$ is in S and converges there to ψ, so 22