hello,
i have two websites built on the same keyword and hosted on the same provider. one of them is 2 years old, the other one was created a few time ago. the first site was on the first page in google search.
now, the second site is placed in first places in google search but the first site disappeared. some times they shift back. the second one disappeared and the first site is in first places.
can i have both toghether on first page in google search?

I've seen this type of behaviour frequently lately. It's not easy to swamp the lead pack of keyphrase compeitors but can happen. When the search engine bounces rom one to another in a networked SERP approach it's the search engine realizes that both sites mean basically the same thing, have very similar corporate agendas (they market the same business in the same way), their on-site ranking factors parallel (Titles, keywords tags, images etc.) and are probably closely intertwined from a linking perspective (lotsa' cross-linking). Because of the similarities, the search engine struggles to determine which webpage is more valuable for your keyphrase search.

You can get them both up in rankings simultaneously but you'll have to radically refocus one of them. You have to create two uniquely devised web presentations.

It is called sandbox phenomenon , even the new website will disappear after few weeks.

I'm getting the impression that we're talking about two web sites both two years old, battling it out for authoritativenes, the search engine is trying to determine which is more credible. Now. I could be wrong in my impression and a brand new web site could now be in suspension, pending evolving proof of its own importance.

no, one of them is two years old and one has several months