Two confirmed cases of Guillain-Barré syndrome linked to the Zika virus have been reported in the U.S., health authorities told TIME on Thursday.

The link between Zika and the birth defect microcephaly has received much attention. But health experts are also concerned about the link between the virus and Guillain-Barré syndrome (GBS), a condition where the immune system starts attacking the body’s nerves, which leads to weakness that can eventually result in temporary paralysis. In some cases, the disorder can interfere with breathing.

The U.S. Centers for Disease Control and Prevention (CDC) confirmed to TIME that there have been two cases of GBS in the U.S. in people who also tested positive for Zika virus. “I think we can say that the link between Zika and Guillain-Barre looks strong and would not be at all surprising,” says Dr. Tom Frieden, director of the CDC. “We’ve seen similar postinfection complications after many different infections, including some that are quite similar to Zika. That is a link that’s getting stronger.”

One reported GBS case has been linked to Zika in Puerto Rico, which the CDC described in a recent report. In that case, a 37-year-old man developed a rash that was followed by symptoms of weakness. It was confirmed he had GBS and tested positive for the Zika virus. The CDC has not released details about the two people with GBS linked to Zika in the continental U.S.

Like microcephaly, the link between GBS and Zika appears strong, but is it not yet confirmed. More research is needed to understand the link.

So far, there are 84 travel-associated cases of Zika in the U.S., and Puerto Rico has reported more than two dozen locally transmitted cases. “We really do expect that there will be hundreds, if not thousands, of travel-associated cases in the U.S.,” says Frieden. “There are more than 40 million travelers in the U.S. to Zika affected countries every year — that’s a lot of people.” The CDC says it is aware of pregnant U.S. women who became infected with Zika while traveling.

As TIME previously reported, the CDC recently completed the initial stages of a study looking at the possible connection between GBS and Zika in Brazil. The investigation was launched after the Brazil Ministry of Health reported higher than normal cases of GBS amid the Zika outbreak. The researchers at the CDC knew to be on the lookout for possible cases of GBS, since a similar pattern was observed during a 2013 Zika outbreak in the South Pacific.

Although the findings from the study are still very preliminary, the lead researcher told TIME that while it’s normally rare to see the disease in young people, the CDC researchers in Brazil found a high number of cases among people in their 20s, 30s and 40s who were otherwise healthy.

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