Single sample:

<h:form>

     <a4j:jsFunction name="click" render="flashText1">

          <a4j:param name="eventName" assignTo="#{flash.luhs1}"/>

     </a4j:jsFunction>

     <a4j:jsFunction name="change" render="flashText2">

          <a4j:param name="eventName" assignTo="#{flash.luhs2}"/>

     </a4j:jsFunction>

     <a4j:jsFunction name="clear" render="flashText1 flashText2">

          <a4j:param name="eventName1" assignTo="#{flash.luhs1}"/>

          <a4j:param name="eventName2" assignTo="#{flash.luhs2}"/>

     </a4j:jsFunction>

</h:form>

<rich:panel header="checkbox.">

     <h:outputText id="flashText1" value="#{flash.luhs1}"/>

     <h:outputText id="flashText2" value="#{flash.luhs2}"/>    

     <br/>

     <h:selectBooleanCheckbox value="true" onclick="alert('click')" onchange="alert('change')"/> alert check

     <br/>

     <h:selectBooleanCheckbox value="true">              

          <a4j:ajax event="click" oncomplete="click('click')" onbegin="clear('1','0')"/>

          <a4j:ajax event="change" oncomplete="change('change')" onbegin="clear('0','1')"/>

     </h:selectBooleanCheckbox>print check

</rich:panel>

invoke the method of backing bean:

<a4j:ajax event="click" listener="#{obj.method1(param1)}" render="comp"/>

class obj{

     public void method1(String param1){

          ...

     }

}