Oncogene-induced replicative stress activates an Atr- and Chk1-dependent response, which has been proposed to be widespread in tumors. We explored whether the presence of replicative stress could be exploited for the selective elimination of cancer cells. To this end, we evaluated the impact of targeting the replicative stress-response on cancer development. In mice (Mus musculus), the reduced levels of Atr found on a mouse model of the Atr-Seckel syndrome completely prevented the development of Myc-induced lymphomas or pancreatic tumors, both of which showed abundant levels of replicative stress. Moreover, Chk1 inhibitors were highly effective in killing Myc-driven lymphomas. By contrast, pancreatic adenocarcinomas initiated by K-Ras^G12V showed no detectable evidence of replicative stress and were nonresponsive to this therapy. Besides its impact on cancer, Myc overexpression aggravated the phenotypes of Atr-Seckel mice, revealing that oncogenes can modulate the severity of replicative stress-associated diseases.