Are Eastern Europeans/Slavs Eurasians or have Asian genes in them?

[Silver Rusher]

Well, it depends what you mean by 'Slav', because many of the peoples who are commonly referred to as Slavs are not ethnically Slavs, just people speaking Slavonic languages. Southern Slavs, for example, are mostly steppe tribes that settled in that area and learned slavonic languages from either people they lived near early on, invaders or the sparse Slavic population of the regions they settled.

Croats are thought to be descended from Alans, but this is only a theory. Otherwise, the origins of the Croat tribe are unknown.
Serbs were a Sarmatian tribe.
Bulgarians were a Turkic people (another branch of the Bulgar tribe was the Volga-Bulgarians, who as you may have known settled along the banks of the Volga and converted to Islam).

However, people like Czechs, Poles and Russians are all descended from the original Slav ethnicity. Even these people, though, are incredibly varied in terms of their gene pool. Part of the point I was making earlier is that even within nationalities that are considered descended from the proto-Slavonic people, a huge history of invaders, natives, settlers and migratory peoples means that Slavs share very few genetic traits.

EDIT: Eastern European is also a dodgy term. Hungarians and Romanians are not Slavs, nor do they typically have proto-Slav genes.

EDIT2: Also, a caucasian (or caucasoid) is one of the 5 distinct races, incorporating people from Europe, through the Middle East and North Africa and right down to India. For your information, others are:

Mongoloid: Inhabitants of Asia (excluding caucasian areas) and natives of the Americas
Negroid: Originate in central Africa but also live in large populations in the Americas, Europe etc.
Capoid: Disputed, but usually agreed to be a seperate race from Negroids, they mostly inhabit southern Africa.
Australoid: Commonly referred to as 'Aboriginals' and live mostly in Australia but inhabit parts of India also.