Given a pair a commuting CP-semigroups Θ and Φ acting on von Neumann algebra M in B(H), we are interested in constructing a pair of commuting E-semigroups α and β, acting on some larger von Neumann algebra R in B(K), where K contains H, such that for all s, t > 0 and all T in R, Θs(Φt(PHT PH)) = PHαs(βt(T))PH. In other words, we are interested in constructing in E-dilation to a two-parameter CP-semigroup. In this talk we will show that if Θ and Φ are unital and strongly commuting, then an E0-dilation exists (the definition of strong commutation is technical, and will be explained in the talk. For now it will be enough to say that there are many pairs of strongly commuting CP-semigroups). We will also discuss our progress in the construction of an E0-dilation to a k-tuple of strongly commuting CP0-semigroups. This work is part of the author’s PhD. thesis, done under the supervision of Baruch Solel.