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Your controller should extend EController. You create a behavior by extending EControllerBehavior and implement one of above listed methods. Inside a handler you have $event instance, which has following properties:

in beforeRender: $event->view.
in afterRender: $event->view and $event->output.
in beforeAction: $event->action.
in afterAction: $event->action.

Also, in beforeAction and beforeRender you can set $event->isValid property to allow or deny corresponding processing.

Also, it supports actions inside behaviors.

Example

// main.php
	'import' => array('ext.controller-events.*'),
// CrudController.php
<?php
class CrudController extends EControllerBehavior {
	public function beforeAction(EControllerEvent $event) {
		if (rand(0, 1))
			$event->isValid = false;
	}
}