We continue to study the credit risk model of a financial market introduced in [19] in which the dynamics of intensity rates of two default times are described by linear combinations of three independent geometric Brownian motions. The dynamics of two default-free risky asset prices are modeled by two geometric Brownian motions which are dependent of the ones describing the default intensity rates. We obtain closed form expressions for the no-arbitrage prices of some first-and second-to-default European style contingent claims given the reference filtration initially and progressively enlarged by the two successive default times. The accessible default-free reference filtration is generated by the standard Brownian motions driving the model.