Rather than toggling back and forth between two different static [`set`][1] elements, you can use a single [`animate`][2] that switch between hidden and visible indefinitely.  

Then you also don't need to worry about wiring up the begin timing with the end event of another named animation






    <svg xmlns="http://www.w3.org/2000/svg">
      <circle fill="red" cx="50%" cy="50%" r="30" stroke="black">
        <animate attributeType="CSS"
                 attributeName="visibility"
                 from="visible" 
                 to="hidden"
                 dur="1s"
                 repeatCount="indefinite"/>
      </circle>
    </svg>



[1]: http://www.w3.org/TR/2001/REC-smil-animation-20010904/#setElement
[2]: http://www.w3.org/TR/2001/REC-smil-animation-20010904/#animateElement

I have:

    <set attributeName="visibility" attributeType="CSS" to="visible" begin="5s" fill="freeze"/>
    <set attributeName="visibility" attributeType="CSS" to="hidden" begin="10s" fill="freeze"/>

I want the loop to perform these instructions.