Final answer:
Neisseria meningitidis and Haemophilus influenzae are the two gram-negative bacteria commonly responsible for bacterial meningitis.
Step-by-step explanation:
The two gram-negative bacteria that are frequent causes of bacterial meningitis are Neisseria meningitidis and Haemophilus influenzae. Neisseria meningitidis, also known as the meningococcus, primarily affects children and young adults and is transmissible between individuals. Haemophilus influenzae type b (Hib) was once the leading cause of bacterial meningitis in children but is now less common in countries with routine childhood Hib vaccines. Both pathogens are able to cross the mucous membranes and enter the bloodstream, potentially leading to severe infections like meningitis.