"Rival teams" refers to two or more groups or organizations competing against each other in a sport, game, or competition. They are opponents with a strong desire to outperform and beat each other. Full definition
By the end of that decade, a significant milestone was passed when the gene responsible was identified after a hard - fought race by rival teams. (newscientist.com)
We buying teenagers for the future, only then to sell em in the end to rival teams who come then to hunt us down. (justarsenal.com)
After the race, praise for his performance was flying in from all corners - even rival teams - as everyone acknowledged what a hell of a drive he'd put in. (wtf1.com)