This most commonly occurs between 5-14 days after transplantation but can occur anytime within the first 3 months, or even longer when immunosuppresion is reduced, or the immune system is activated by an unrelated event such as a viral infection.
In contrast with hyperacute rejection it is purely cell-mediated and is what is seen in the first set response.
About 10% of people will develop acute rejection following kidney transplantation. Most of these will respond to boosts of immuno-suppressant therapy. However, about 5% will loose the kidney due to acute rejection.