When the admiral draws two destiny cards and selects one after a jump, is he allowed to show the cards to the other players, or is it obligatory to hide these cards?

You presumably mean "Destination" cards. No, the Admiral cannot show the cards to the other players, and in fact is not allowed to discuss the card he doesn't choose at all. (Except for claiming that the card he chose was better, of course!) This is to facilitate cylon play -- if the chosen Destination looks bad, the other players need to figure out whether they believe the Admiral when he says the other card was worse, or whether a cylon Admiral is trying to subtly sabotage their chances.

I thought so too, but where in the rules does it say that?

(and I did indeed mean destination cards )

It will be in the secrecy rules side panel, or the destination deck description

Page 13:

2. Choose Destination: The Admiral draws two cards from
the Destination deck, chooses one, and places the other
on the bottom of the deck.

P. 20

Cards in the Decks: If a player has the ability to look
at cards on the top of a deck, he may not disclose
specific information about that card.

Hi

I have similar question. What about Crisis Cards? If current player/admiral/president has to choose do he inform other players what posibilities are available or he keep that in secret?

You cannot show the cards you are chosing from, and depending on how you observe secrecy rules, you can share zero to some information about your choice. Check out the errata for secrecy rules.

Yes if I have some two cards to choose. But I was asking about one Crisis Card with choose option...

Laoghan said:

The card is played face-up. Of course all options are public knowledge.

That is all I wanted to know. Thanks

Yep, as a Cylon it is your task to make the wrong choice perfectly reasonable.