Nuclear instability occurs spontaneously in a typically very small proportion of cells of every individual, even in crop varieties. Of greatest interest to the cereal breeder are instabilities in the germ line, which produce off-types among progeny, or in the endosperm, which reduce grain quality. Nuclear instabilities in crop plants merit cytological investigation for several reasons: first, to ensure that biologically possible standards of genetical purity are set for varieties in agriculture; secondly, because once understood, nuclear instability may be usefully applied in plant breeding; thirdly, because nuclear instability is thought to have played a major role in crop plant evolution - understanding the past may help in predicting which new genome combinations will be successful crop species; fourthly, because failure to achieve adequate nuclear stability has played a major role in preventing so many potentially useful plants from becoming crops. These points are illustrated mainly by reference to three different nuclear instabilities, namely: (1) haploid barley production by genome elimination in some Hordeum vulgare x H. bulbosum crosses; (2) the action of the tri gene in barley to produce about 50% diploid embryo sacs; (3) aberrant endosperm development in hexaploid triticale. Improved seed type in triticale has been achieved by a controlled reduction in rye telomeric heterochromatin. This approach may open the way for a new type of plant breeding, selecting for nucleotypic variation in the amount of non-coding DNA sequences. Understanding the cellular mechanisms responsible for nuclear stability (or instability) is essential if controlled plant modification based on precise nuclear engineering is to become possible. This understanding can come only from sustained fundamental research.