Two agile software development methodologies :

The most widely used methodologies based on the agile philosophy are XP and Scrum.

These differ in articulars but share the iterative approach described above.

XP :

XP stands for extreme programming. It concentrates on the development rather than managerial aspects of software projects. XP was designed so that organizations would be free to adopt all or part of the methodology.

XP development :

XP projects start with a release planning phase, followed by several iterations, each of which concludes with user acceptance testing. When the product has enough features to satisfy users, the team terminates iteration and releases the software.