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Dareus was handed the ban for violating the league's Policy and Program for Substances of Abuse.
The news comes a further blow to a Bills defense that will be without first-round pick Shaq Lawson until at least Week 6 because of shoulder surgery and second-round selection Reggie Ragland for the entirety of the season after he tore his anterior cruciate ligament.
Defensive tackle Kyle Williams is also hobbled with a knee injury, while another Buffalo linebacker, Manny Lawson, returned to practice on Tuesday after suffering a partially torn pectoral muscle, but is facing a suspension stemming from a domestic violence incident.
Running-back Karlos Williams will also miss the first quarter of the season along with Dareus for violating the substance-abuse policy.
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"We are very disappointed Marcell chose to put himself first, before his team-mates, coaches and the rest of the organisation through his recent actions," the Bills said in a statement.
"From ownership down we have made it clear his behaviour is unacceptable. We will continue to take the necessary steps to work with him in order that he adheres to the policies set forth by our league.
"As an organisation, we will move forward with our preparations for the start of the 2016 NFL season in Baltimore on September 11."