Herein we have considered the types of tumor stem cell heterogeneity that might account for (a) fluctuating degrees of response to chemotherapy in similarly treated individuals bearing a particular neoplasm, and (b) classifications of cancers by chemotherapeutic effect. Fluctuating ratios of T/R to T/O stem cells, as predicted by the mutation theory, will account for (a). In different circumstances at least three phenomena might account for (b): growth fraction differences, differences in T/R to T/O stem cell ratios, or differences with respect to pharmacologic sanctuaries. T/R stem cells are primarily responsible for the failure of the best available chemotherapy to cure responsive, refractory, and very refractory experimental neoplasms. The data examined suggest that differences in the T/R to T/O stem cell ratios in different types of cancer may account for their being classed as responsive, refractory, or very refractory. If this be true, what might underlie such differences? The most obvious possibilities are: higher mutation rates to a drug-resistant state in refractory cancers, or some sort of "natural selection" of diverse T/R stem cells in refractory cancers.