In 2009, increasing Whitney properties were defined by F. Orozco and give results and examples of topological increasing Whitney properties. In this talk we define Whitney persistent and locally Whitney persistent properties. We present results and examples of continua and topological properties to establish relations between these concepts and those of Whitney and increasing Whitney properties. This is a joint work with José Gerardo Ahuatzi-Reyes and Norberto Ordoñez-Ramírez.