• Are age \>= 12 years old at screening (Visit 1).

• Have a primary aHUS, diagnosed clinically, and have ADAMTS13 activity \> 5% in plasma. Participants are eligible with or without a documented complement mutation or anti-CFH antibody. Participants are categorized according to their response to plasma therapy (plasma exchange or plasma infusion):

‣ Plasma therapy-resistant aHUS participants must have all of the following:

• Screening platelet count \< 150,000/μL despite at least four plasma therapy treatments in a 7-day period prior to screening

∙ Evidence of microangiopathic hemolysis (at least one of:

∙ presence of schistocytes,

‣ serum LDH \> 1.5 times upper limit of normal (ULN), and

‣ haptoglobin \< LLN)

∙ Serum creatinine \> ULN

⁃ Plasma therapy-responsive aHUS participants must have all of the following:

• Have a documented history of requiring plasma therapy to prevent aHUS exacerbation defined as all of the following:

‣ decrease in platelet count \> 25% when plasma therapy frequency has been decreased (including discontinuation of plasma therapy)

⁃ LDH \> 1.5 times ULN when plasma therapy frequency has been decreased (including discontinuation of plasma therapy)

⁃ Have received plasma therapy at least once every 2 weeks at an unchanged frequency for at least 8 weeks before first dose of OMS721

• If sexually active and of childbearing potential, must agree to practice a highly effective method of birth control until the end of the study, defined as one that results in a low failure rate (i.e., less than 1% per year) when used consistently and correctly, such as implants, injectables, combined oral contraceptives, some intrauterine devices, sexual abstinence or vasectomized partner.

• Do not have access to eculizumab treatment, have not derived therapeutic benefit from eculizumab treatment, or have not been able to tolerate eculizumab treatment.