The effects of adding low‐molecular‐weight homopolybutadiene (hB) into solutions of a styrene‐butadiene (SB) diblock copolymer inn‐tetradecane (C14) on their rheology and microdomain structure are examined. In solutions of SB in C14, SB molecules form micelles with precipitated S blocks as the rigid cores and soluble B blocks as the cilia. These micelles form a macrolattice. The macrolattice is stabilized by a thermodynamic force that tends to keep the local concentration of B segments in the matrix phase as uniform as possible. Such a micellar solution having a macrolattice exhibits nonlinear dynamic behavior as well as plastic flow in steady shear. When hB is added to the solution, the solution loses its plasticity and becomes a linear viscoelastic liquid and the macrolattice becomes disordered. The mechanism of such a transition may be a result of the fact that the added hB acts as a buffer to compensate for the local concentration change induced by the lattice deformation and makes the macrolattice unstable. Solutions of SB in pure hB (with concentration below 35 wt % SB) are no longer plastic but linear viscoelastic. The solutions exhibit some slow relaxation processes, which are often called the second plateau. The mechanism of the SB in hB solutions that exhibit the second plateau is also discussed.