We demonstrate two explicit cooperative two-way quantum communications based on the Brown state in a forward-and-backward fashion. One realizes the duplex exchange of an arbitrary unknown state and a certain state between Alice and Bob with the aid of the trusty Charlie via the partial entanglement analysis. The other realizes the half-duplex exchange of arbitrary unknown states. Their securities are both guaranteed due to the fact that each participant either faithfully recovers the transmitted unknown states after performing some suitable unitary operations in a deterministic way or, in a case of any irregularity, generates no results. In addition, the present half-duplex cooperative quantum communication can be similarly extended for transmitting arbitrary unknown states via the two-way quantum teleportation based on the generalized Brown-like state in a probabilistic way.