Many potent antiviral drugs have been developed against HIV-1, and their combined action is usually successful in achieving durable virus suppression in infected individuals. This success is based on two effects: additive or even synergistic virus inhibition and an increase in the genetic threshold for development of drug resistance. More recently, several genetic approaches have been developed to attack the HIV-1 genome in a gene therapy setting. We set out to test the combinatorial possibilities for a therapy based on the CRISPR-Cas9 and RNA interference (RNAi) mechanisms that attack the viral DNA and RNA, respectively. When two different sites in the HIV-1 genome were targeted, either with dual CRISPR-Cas9 antivirals or with a combination of CRISPR-Cas9 and RNAi antivirals, we observed additive inhibition, much like what was reported for antiviral drugs. However, when the same or overlapping viral sequence was attacked by the antivirals, rapid escape from a CRISPR-Cas9 antiviral, assisted by the error-prone nonhomologous end joining (NHEJ) DNA repair machinery, accelerated the development of cross-resistance to the other CRISPR-Cas9 or RNAi antiviral. Thus, genetic antiviral approaches can be combined, but overlap should be avoided.