Usually, drug companies get years of exclusive marketing rights before a drug runs into generic competition, but that's not the case for Johnson & Johnson (NYSE: JNJ) this time around. About a month after it was able to persuade the FDA to allow Zyrtec and its drugged-up cousin Zyrtec-D to be sold over the counter, Zyrtec is already running into generic competition.

On Friday, both Perrigo (Nasdaq: PRGO) and Mylan (NYSE: MYL) announced that the FDA had approved their generic versions of Zyrtec. The competition will come quickly, as Mylan said that it will begin shipping the drug immediately.

J&J acquired the rights to the over-the-counter version when it purchased Pfizer's (NYSE: PFE) consumer health-care business last year, but had to wait until the patent ran out before it could begin selling the drug. Pfizer's $1.6 billion Christmas gift to J&J was that it would finally be able to start selling Zyrtec on Dec. 25.

With generic competition, J&J won't be able to fetch nearly as high a price for the drug, but the over-the-counter status should help it reach a larger audience than Pfizer's prescription version did. In its new shelf spot, it will have to compete with other over-the-counter antihistamines including Schering-Plough's (NYSE: SGP) Claritin and Johnson & Johnson's own Benadryl.

For a company the size of J&J, a little added generic competition isn't going to have too large an effect. But it is a sign of the growing patent problem for Big Pharma in general and J&J specifically -- both its antipsychotic Risperdal and its Alzheimer's medication Reminyl lose patent protection next year.

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Fool contributor Brian Orelli, Ph.D., doesn't own shares of any company mentioned in this article. Pfizer is a pick of the Inside Value newsletter. The Fool has a disclosure policy.