This situation came up in a tournament that i was watching. if a player activates ceasefire,but his opponent responds by countering with his ceasefire, does his ceasefire's effect disappear?

No, they both would resolve. I think the opponents one ses off first then the next one (your ceasefire). The first one would flip ll fd monsters face-up. Then the second one would just deal the same amount of damage unless other cards were activated.

-Marik-

Let me back-up and clarify what Ishtar is saying.

There are two pre-requisites for Ceasefire to properly activate:

1) There must be at least one face down monster on the field

2) There must be at least one effect monster face up on the field.

If one of those two situations happen to be on the field, then Ceasefire will have proper activation and will still resolve properly (unless something is put on the chain that negates Ceasefire). Whether it does any damage or not is totally up to the field at the time of resolution.

i have a question, where does it say that there has to be a face-down card? all it says is to flip all fd cards face-up. That doesn't sound to me like there must be a face-down, just that if there are any face down, then flip them up. it has the same type of flip wording that SoRL has, in that respect. doesn't there just need to be a monster on the field, not a face-down?

Since Kevin hasnt gotten around to Writting Ceasefire up not that there is real need to...

These are the Rulings from Yugioh-card.com

The "Spell Absorbing Life" is like "Ceasefire" except it gives you Life Points instead of damaging your opponent

You can activate "The Spell Absorbing Life" as long as there is at least 1 face-down monster on the field, OR there is at least 1 effect monster on the field (or both).