Block copolymers consisting of two segments of random copolymers of N-alkylacrylamides have been synthesized by a sequential reversible addition-fragmentation chain transfer (RAFT) polymerization. The copolymers in the form of A nB m-b-A pB q have been made of two blocks of N-n-propylacrylamide (nPA) and N-ethylacrylamide (EA) of different compositions to obtain polymers with stepwise thermosensitivity. The control of the RAFT polymerization was confirmed by studying the kinetics of the copolymerization process. The block random copolymer, poly(nPA x-co-EA 1-x)-block-poly(nPA y-co-EA 1-y), is well-defined and has a low polydispersity. The cloud points of the random copolymers can be tuned by varying the chemical composition of the copolymers. The diblock copolymer exhibited a two-step phase transition upon heating to 41.5 and 53.0 °C, corresponding to the cloud points of the individual blocks. Dynamic light scattering experiments also showed the stepwise aggregation properties of the copolymer in aqueous solutions.