House Republicans this week will vote for the first time in their running eight-year majority on the divisive issue of legalizing certain undocumented immigrants.

The House is expected to hold Thursday votes on two immigration bills that address the legal status of so-called Dreamers, young undocumented immigrants brought to the U.S. as children, as well as border security and enforcement.

One bill is a generally more conservative measure by House Judiciary Chairman Robert W. Goodlatte that Republicans have tried for months to coalesce behind. It still appears to lack enough support to pass, with many moderate GOP lawmakers opposed because they don’t feel like it does enough for Dreamers.

The second bill is more of a compromise measure, as it was negotiated by moderate and conservative Republicans representing a broad cross section of their conference. Those negotiations came together under the threat of a discharge petition that would have forced a winner-takes-all series of immigration votes that would favor proposals supported by a minority of Republicans and a majority of Democrats.

Most — if not all — Democrats are expected to oppose the two GOP bills. House Minority Leader Nancy Pelosi is urging her caucus to reject both.