It is demonstrated that recent experimental results on high spin states of 128,129Ba offer substantial new evidence for static octupole deformation in these nuclei.PACS: 21.60Ev; 27.60 +j Over the last decade, a large amount of experimental evidence supporting the presence of static octupole deformation in two regions of the Periodic Table near A= 150 and 224 has been accumulated. Much of this evidence has been found in studies of high angular momentum behavior of nuclei. Even-even nuclei having static octupole deformation are expected to possess yrast spectra that form A J= 1 rotational bands which obey the J(J+l) rule and in which the states alternate in parity. Octupole deformation in the adjacent odd-A and odd-odd nuclei is also signalled by a characteristic behavior -the existence of closely spaced "parity doublets" of states with equal spins and opposite parities.Recently, both theoretical and experimental efforts have been mounted to identify octupole deformed nuclei in other mass regions (for example, see [-ll). A phenomenological approach to identifying the best candidates for octupole deformation on the basis of the systematic behavior of 3[-states has also been proposed 1-2], and may be summarized as follows. Nuclei which achieve static octupole deformation in the A = 150 and 224 regions occur near local minima (with respect to both N and Z) for 3i-state energies. Consequently, it can be conjectured that the nuclei which are the best candidates for static octupole deformation in a particular region are those which are near the local %-state minimum. A survey of the energies of known 3~ states [-3] in the A= 130 region (Fig. 1) demonstrates that these energies reach minima near N = 64 and Z = 64. From this information, it can be extrapolated that the lowest 31 state energies occur near 128Gd (N=Z= 64), and that the nuclei in this vicinity are the best candidates for static octupole deformation in the region.A survey of high spin spectra of nuclei near N=Z=64 revealed I-4] that in both 126Ba and 128Ba two rotational bands of opposite parity occur which are interleaved in an alternating parity J(J-t-l) pattern in the angular momentum range J= 11-17. This behavior may be interpreted as a signature for the presence of static octupole deformation. However, in order to make a convincing argument that octupole deformation is present in this region it is necessary to identify the signatures of this deformation among a neighborhood of nuclei, including odd-A and odd-odd nuclei, and over a broad range of angular momenta. In the present article, recent high spin data on lZS, t29Ba are analyzed in order to support the octupole deformation argument in this way. First, it is demonstrated that the most recent data on 128Ba [-5] reveal that the alternating parity rotational sequence discussed in [-4] extends up to J = 29, suggest-