The two incidents took place in Streetly, and saw officers and dogs from West Midlands Police patrol the area.
The first incident saw an 18-year-old man present at hospital in Birmingham with stab wounds in his back.
The incident happened on Icknield Close, just off Manor Road, and it is believed the victim was stabbed while sitting in a car.
It is then thought that three cars tried to drive at the person who carried out the stabbing, with one missing the man, but hitting a wall in Manor Road.
A number of armed officers, police dogs, marked and unmarked police cars attended the scene, which saw a silver Peugeot left abandoned on the road.
A spokesperson for West Midlands Police said: "We’re investigating after an 18-year-old man presented at hospital with stab wounds this afternoon.
"Officers are currently carrying out enquiries around Icknield Road and Manor Road, Streetly, where it’s believed there was disorder which could be linked to the stabbing.
"The teenager has suffered back injuries which are not believed to be life-threatening.
"Anyone with information is asked to contact us via Live Chat, or by calling 101. Quote log 1830 of 26 September."
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org