We describe in this paper the synthesis of a novel series of anilino-2-quinazoline derivatives. These compounds have been screened against a panel of eight mammalian kinases and in parallel they were tested for cytotoxicity on a representative panel of seven cancer cell lines. One of them (DB18) has been found to be a very potent inhibitor of human "CDC2-like kinases" CLK1, CLK2 and CLK4, with IC values in the 10-30 nM range. Interestingly, this molecule is inactive at 100 μM on the closely related "dual-specificity tyrosine-regulated kinase 1A" (DYRK1A). Extensive molecular simulation studies have been performed on the relevant kinases to explain the strong affinity of this molecule on CLKs, as well as its selectivity against DYRK1A.