DyCu and YCu are representatives of the family of CsCI-type B2 rare earth intermetallic compounds that exhibit high room temperature ductility. Structure, orientation relationship, and morphology of the martensites in the equiatomic compounds DyCu and YCu are examined using transmission electron microscopy (TEM). TEM studies show that the martensite structures in DyCu and YCu alloys are virtually identical. The martensite is of orthorhombic CrB-type B33 structure with lattice parameters a = 0.38 nm, b = 1.22 nm, and c = 0.40 nm. (02 (1) over bar) twins were observed in the B33 DyCu and YCu martensites. The orientation relationship of B33 and B2 phases is (11 (1) over bar)[112]B33 parallel to (110)[001]B2. The simulated electron diffraction patterns of the B33 phase are consistent with those of experimental observations. TEM investigations also reveal that a dominant orthorhombic FeB-type B27 martensite with lattice parameters a = 0.71 nm, b = 0.45 nm, and c = 0.54 nm exists in YCu alloy. (I (1) over barI) twins were observed in the B27 YCu martensite. The formation mechanism of B2 to B33 and B2 to B27 phase transformation is discussed.