The human immunodeficiency virus (HIV) infects a wide range of human cells. Cell entry is mediated through the CD4 receptor and a variety of coreceptors, most importantly the chemokine receptors CCR5 and CXCR4. Some antiretroviral agents selectively inhibit different HIV phenotypes depending on their coreceptor usage. Here, we analyse mathematical models, which describe the in vivo interaction of HIV phenotypes, differing in their coreceptor usage, with two target cell types (naive and memory CD4+ T cells). In particular, we investigate how the selection pressures on CCR5- and CXCR4-using HIV variants change as a result of treatment with coreceptor-specific antiretroviral agents. Our main result is that CXCR4 inhibitors increase the selection pressure in favor of the emergence of CCR5-using variants, thus selecting for coexistence of CXCR4- and CCR5-using variants, whereas CCR5 inhibitors increase the selection pressure against CCR5-using variants, thus selecting against coexistence. These results shed new light on the potential risks and benefits of coreceptor inhibitors.