Propargylamines have gained importance in the area of anticancer research. We synthesized 1-substituted propargylic tertiary amines using the A3-coupling as the key step. Both, solution and solid-phase protocols, were used to provide a library of 1-substituted propargylic tertiary amines with interesting structural diversity. The triple negative breast cancer subtype is the most aggressive and it lacks effective therapeutic options, while pancreatic cancer is one of the neoplasms with worse prognosis and limited therapeutic possibilities. The development of tumor-selective drugs has always been a major challenge in cancer treatment. From our library, two propargylamines displayed a high degree of cytotoxic selectivity. These levels of selectivity give a very interesting perspective for further development of 1-substituted propargylic tertiary amines as new potential chemotherapeutic antitumor agents.