The emergence of SARS-CoV-2 mutations resulting in the S protein amino-acid substitutions N501Y and E484K, which have been associated with enhanced transmissibility and immune escape, respectively, necessitates immediate actions, for which their rapid identification is crucial. For the simultaneous typing of both of these mutations of concern (MOCs), a one-step real-time RT-PCR assay employing four locked nucleic acid (LNA) modified TaqMan probes was developed. The assay is highly sensitive with a LOD of 117 copies/reaction, amplification efficiencies >94 % and a linear range of over 5 log10 copies/reaction. Validation of the assay using known SARS-CoV-2-positive and negative samples from human and animals revealed its ability to correctly identify wild type strains, and strains possessing either one or both targeted amino-acid substitutions, thus comprising a useful pre-screening tool for rapid MOC identification. The basic principles of the methodology for the development of the assay are explained in order to facilitate the rapid design of similar assays able to detect emerging MOCs.