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The Republican Party is the Conservative Party in the US. (Techinally there is no Conservative "Party", but Republicans are considered Conservatives)
The Conservative Party of CanadaStephen Harper is part of the Conservative party and has been from 2003 to present
The Progressive Conservative party.The Progressive Conservative party.The Progressive Conservative party.The Progressive Conservative party.The Progressive Conservative party.The Progressive Conservative party.The Progressive Conservative party.The Progressive Conservative party.The Progressive Conservative party.The Progressive Conservative party.The Progressive Conservative party.
He is leader of the UK Conservative party.
In the UK, the Conservative party is the main party at the moment, although Conservative is an ideology which many parties share. So it is both.