In most eukaryotes, centromeres assemble at a single location per chromosome. Naturally occurring telocentric chromosomes (telosomes) with a terminal centromere are rare but do exist. Telosomes arise through misdivision of centromeres in normal chromosomes, and their cytological stability depends on the structure of their kinetochores. The instability of telosomes may be attributed to the relative centromere size and the degree of completeness of their kinetochore. Here we test this hypothesis by analyzing the cytogenetic structure of wheat telosomes. We used a population of 80 telosomes arising from the misdivision of the 21 chromosomes of wheat that have shown stable inheritance over many generations. We analyzed centromere size by probing with the centromere-specific histone H3 variant, CENH3. Comparing the signal intensity for CENH3 between the intact chromosome and derived telosomes showed that the telosomes had approximately half the signal intensity compared to that of normal chromosomes. Immunofluorescence of CENH3 in a wheat stock with 28 telosomes revealed that none of the telosomes received a complete CENH3 domain. Some of the telosomes lacked centromere specific retrotransposons of wheat in the CENH3 domain, indicating that the stability of telosomes depends on the presence of CENH3 chromatin and not on the presence of CRW repeats. In addition to providing evidence for centromere shift, we also observed chromosomal aberrations including inversions and deletions in the short arm telosomes of double ditelosomic 1D and 6D stocks. The role of centromere-flanking, pericentromeric heterochromatin in mitosis is discussed with respect to genome/chromosome integrity.