Clean your marmoleum flooring with a diluted mixture of all-purpose linoleum floor cleaner. Mix the cleaner with water in a bucket, according to the package directions, then clean the buckled area with a rag. Allow the flooring to air-dry completely before continuing.
Cut a slit through the center of the buckled area with a utility knife. Use a straightedge to keep the line even while cutting through the marmoleum. Carefully peel back the two edges of the slit.
Apply low heat from a blow dryer to the underside of the marmoleum and the newly exposed subfloor to loosen the existing adhesive. Scrape away the softened adhesive with a plastic paint scraper. Wipe away any remaining residue with a rag soaked in denatured alcohol.
Spread a thin layer of flooring adhesive onto the exposed subfloor with a small paintbrush. Press the split marmoleum flooring onto the adhesive-covered subfloor and hold it in place for at least 30 seconds.
Cover the repaired section of marmoleum with a dish towel then place a weighted object, such as a heavy book or brick, on top. Keep the weighted object there for at least 48 hours.
Remove the weighted object and dish towel from the marmoleum flooring. Remove any adhesive that seeped through the slit with a rag soaked with denatured alcohol.