UPDATE 1-Genzyme outsources certain processes to Hospira

* Genzyme outsources fill, finish manufacturing to Hospira

* Deal aimed at easing Genzyme manufacturing constraints

* Genzyme's shares close up 34 cents at $49.35

BOSTON, Jan 4 (Reuters) - Genzyme Corp GENZ.O said on Monday that Hospira Inc (HSP.N) will conduct the final manufacturing process for several of Genzyme's most important drugs.

The agreement comes as Genzyme wrestles with manufacturing constraints that have led to shortages of two of its biggest-selling products.

Genzyme said Hospira will be responsible for filling and packaging vials of Cerezyme, Genzyme's drug for Gaucher disease; Fabrazyme, for Fabry disease; Myozyme, for the muscle disorder Pompe disease; and Thyrogen, a thyroid drug.

Genzyme was forced last year to temporarily close its manufacturing facility in suburban Boston after the plant was contaminated with a virus. Since then, it has been working to bring the plant into compliance with U.S. regulatory standards.

Genzyme has moved some of its fill and finish operations to its plant in Ireland. The rest is being outsourced to Hospira.

Ultimately, Genzyme hopes to strengthen its facilities at its Allston Landing plant in Boston and resume at least some filling and finishing there.

The company will initially work with Hospira, which provides contract manufacturing services to the pharmaceutical and biotechnology industries, to provide the technical know-how to fill and finish Genzyme's products. Hospira's facility needs to be approved by U.S. regulators and will likely to take six to eight months to secure the approvals and Genzyme is responsible for obtaining them.

Genzyme shares closed up 34 cents, or 0.69 percent, at $49.35 (Reporting by Toni Clarke; editing by Andre Grenon)