diff --git a/SPEC.md b/SPEC.md
index f5afaadc5..d83d758dd 100644
--- a/SPEC.md
+++ b/SPEC.md
@@ -318,4 +318,29 @@ a container.
 | Resume         | Resume all processes inside the container if paused                |
 | Exec           | Execute a new process inside of the container  ( requires setns )  |
 
+### Execute a new process inside of a running container.
 
+User can execute a new process inside of a running container. Any binaries to be
+executed must be accessible within the container's rootfs.
+
+The started process will run inside the container's rootfs. Any changes
+made by the process to the container's filesystem will persist after the
+process finished executing.
+
+The started process will join all the container's existing namespaces. When the
+container is paused, the process will also be paused and will resume when
+the container is unpaused.  The started process will only run when the container's
+primary process (PID 1) is running, and will not be restarted when the container
+is restarted.
+
+#### Planned additions
+
+The started process will have its own cgroups nested inside the container's
+cgroups. This is used for process tracking and optionally resource allocation
+handling for the new process. Freezer cgroup is required, the rest of the cgroups
+are optional. The process executor must place its pid inside the correct
+cgroups before starting the process. This is done so that no child processes or
+threads can escape the cgroups.
+
+When the process is stopped, the process executor will try (in a best-effort way)
+to stop all its children and remove the sub-cgroups.