The loss of ecological memory for the natural stability domain of a site reduces ecosystem resilience and enables alien invasive species to become established more easily. These invasives may eventually create a new ecosystem with its own ecological memory and resilience. These new ecosystems are described here as novel ecosystems and are placed in the context of adaptive cycles. Ecological restoration of urban ecosystems requires removing the ecological legacy of invasive alien species. To be successful, invasive species control must address both internal within patch memory of invasives and external between patch memory.