Neurological and dermatology drugs maker Merz Pharma offered to buy cosmetic products maker Obagi Medical Products for $383.5 million, topping a bid by Canada's Valeant Pharmaceuticals International .

Merz's $22-per-share bid represents a premium of 11% to Valeant's offer of $19.75.

Shares of Obagi, which makes skin care products to treat signs of aging, acne and sun damage, were trading above Merz's offer price at $22.91 at midday, suggesting that some investors expect a bidding war.

Analysts ruled out the possibility, saying the offer was fairly valued. "I thought that (Valeant's) $19.75 was also a good offer for Obagi given that it is a company that is growing at about 7%, and it is kind of an old product line," Stifel Nicolaus & Co analyst Annabel Samimy said.

Germany-based Merz, which makes prescription and over-the-counter treatments for neurological and metabolic disorders and dermatology, called Obagi a "natural fit" as it would help it diversify its dermatology portfolio and expand its U.S. presence.

The market for cosmetic treatments is recovering after years of slow growth during the economic downturn that forced people to cut down on discretionary spending.

In November, Allergan, the maker of anti-wrinkle drug Botox, acquired privately held SkinMedica for its topical skincare products.

"Obagi's physician dispensed aesthetic and therapeutic skin care products, like Nu-derm and Obagi-C Rx, appear to have become a sought-after franchise following Allergan's acquisition of SkinMedica," Samimy said.

Valeant, Canada's largest publicly-traded drugmaker, too has been building up its dermatology and aesthetics portfolio in the United States over the past year. It acquired Medicis Pharmaceuticals in December, adding Botox competitor Dysport and other skincare drugs to its line up.

However, Samimy does not expect the Canadian company to start a bidding war over Obagi. "Although Valeant is known for its aggressive M&A appetite, there is a precedent for their desire to stay away from bidding wars."

Last year, Valeant walked away from its offer to buy Ista Pharmaceuticals, which was finally bought by Bausch & Lomb. In 2011, Teva Pharmaceutical Industries outbid Valeant to take over Cephalon.

Privately held Merz was already engaged in discussions with Obagi regarding a potential transaction, when Obagi and Valeant announced their deal on March 20, the German drugmaker said.

Merz said it remained "resolute in acquiring" Obagi, and that it had the necessary cash to fund the deal. Merz also said it is prepared to move forward immediately to complete the deal.

In a separate statement, Obagi said it would evaluate Merz's offer.

Valeant declined to comment.