A 2-clock is connect to (1-tick-delay repeater, on the left) and (2-tick-delay repeater, on the right). Hoppers are connected as to transfer items to the chest on the right.
What I expect is that an item inside the top-chest get through two hoppers to the chest on the right directly (as if the redstone circuit do not exist).
However, the hopper, with 2-tick-delay repeater (right one), can either receive or deposit item at a time (and receiving seems having a higher priority). I expect the hopper to receive and deposit at the same time.
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I extracted the part with problem from my whole setup.

As far as I'm aware, all currently loaded hoppers first perform a "pull" operation, drawing an item from above them. In the same tick, they then all perform a "push" operation, moving an item from their inventory into the inventory pointed to by their output, if it exists. This happens every 8 game ticks, or every 4 redstone ticks.
In your setup, on the first transfer tick, an item is pulled from the upper chest, and then deposited in the second hopper. You would need to wait another 4 redstone ticks for the next hopper tick to move that item from the second hopper into into your second chest – but at the same time, a second item would be pulled from chest #1 and transferred to hopper #2. If you don't want that to happen, you'll have to keep the signal on repeater #1, but off on repeater #2 until that second hopper tick.
@Torabi Hopper #1 is working as expected, the problem is on Hopper #2. Unlike hopper #1, which can pull and push at the same tick, hopper #2 can either receive or deposit one item at a time. Note that both hoppers are fed with 2-clock signal but having different reaction.

That's because hopper #2 is only "receiving" an item because hopper #1 is "pushing" it there, and not "pulling" one, because they can only pull from an inventory above them. This is a duplicate of MC-6162, and thus Works As Intended.
@Torabi Sorry, but I think they are different problem. Items should be deposited by hopper #2 when signal goes off, no matter there is a push (by hopper #1) or a pull (by itself). In my case, there even haven't a pull. Instead, if I set the repeater to 1-tick, hopper #2 work as expected (input signal remains the same pattern).

Hopper #2 has nothing to pull from. So no, there will be no pull. Regardless, there's no guarantee that hopper #2 won't perform its push operation before hopper #1, on any given tick. It's location- and orientation-dependent, which is unfortunate, and hopefully they'll consider that a bug. But I'm still not exactly sure why you expect your setup to work. I don't know that the exact behavior of hoppers has been documented anywhere. It's not clear whether their cooldown timer still runs when they are powered, so that might explain the behavior you're experiencing.
Is this still a concern in the current Minecraft version 1.7.4 / Launcher version 1.3.7 or later? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.
Is this still a concern in the current Minecraft version 14w08a / Launcher version 1.3.9 or later? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases. (BC)
Still a concern in 14w08a. And it should clearly be marked as confirmed.
There is clearly a bug. I think there is a confusion in the term used in this thread, @unknown talked about hopper #2 pulling while there is clearly nothing to pull from. But there is indeed a bug, and it is quite easy to reproduce:
It seems that when hopper #2 receives an item from a push by hopper #1, it become unable to push during the next tick, even if there are already items in it. If you put a stack of 64 items in the chest, you can see hopper #2 stocking the whole stack before starting to empty itself. I also noted that the bug is inconsistent. While happening most of the time, sometimes it doesn't. Put a new stack and it happens again.
I also tried to pass six stacks in this system. Once hopper #2 is filled, it isn't able to accept more items, and start pushing them. But not being full again, hopper #1 will push an item into it, preventing it from pushing again. So hopper #2 will basically alternate constantly between accepting and pushing an item, halving it's normal rate without any apparent reason.
Items will start to pile up in hopper #1 because hopper #2 clearly can't push them at a rate of 2.5 items per second. And once hopper #1 is empty, hopper #2 meets the normal rate again.

Is this still a concern in the current Minecraft version 1.8.1 Prerelease 3 / Launcher version 1.5.3 or later? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.
No response for over a year.
Whats the point of this setup? seems kinda redundant if you want the item to pass through immidiatly