Kei and Yuri were originally junior auxiliary agents in the Worlds Works and Welfare Agency (3WA) when the two were paired together under the codename Lovely Angels, Kei was coming off her fourth probation for something she had done, and Yuri's dating exploits were common knowledge, naturally the two had an instant dislike for each other when they met.

At first, Kei and Yuri refused to work with each other, and Kei even resigned from the 3WA. However, when the Siren crisis erupted, Kei returned. This was decidedly a good thing, as Yuri's ditzy new partner, Lily, had abruptly quit just as the response to the crisis started, and Kei's return came just in time, as Yuri was about to be killed by Waldess.

Afterwards, the two continued to work together, although they earned their nickname, the Dirty Pair because of all the collateral damage the two (unintentionally) cause in the completion of their cases. And even though the two now get along with one another, they continue to bicker and complain to each other.

Source: Wikipedia

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Alternative version: Dirty Pair