Sunny's question of March 4, 2000:

"Could you keep your eyes open for the bag?" and "Could you keep an eye on the bag?" Are they the same?

Nope, but they are related in that one deals with a lost object and the other deals with the protection of an object so that it does not get stolen.

The first one ("Keep your eyes open for ~ ") is used when asking someone to try to notice if a lost item is around. I might use this expression if I lose my keys at the school. I could say:

Could you please keep your eyes open for my keys? I think I lost them here this morning.

The second one ("Could you keep an eye on ~ ?") is a request to another person to watch something of yours while you are not there. For example, I might ask you to watch my knapsack while I step outside to make a phone call. In this case I might say:

Sunny, could you keep an eye on my knapsack while I make a quick phone call?