In this paper, we try to generalize ultraproducts in the category of locally convex spaces. To do so, we introduce D-ultracolimits. It is known [7] that the topology on a non-trivial ultraproduct in the category T

of topological vector spaces and continuous linear maps is trivial. To generalize the category Ba

of Banach spaces and linear contractions, we introduce the category L

of vector spaces endowed with families of semi-norms closed underfinite joints and linear contractions (see Definition 1.1) and its subcategory, L

determined by Hausdorff objects of L

. It is shown that L

contains the category LC of locally convex spaces and continuous linear maps as a coreflective subcategory and that L

contains the category Nor

of normed linear spaces and linear contractions as a coreflective subcategory. Thus L

is a suitable category for the study of locally convex spaces. In L

, we introduce

(I.

) for a family (

)

of objects in L

and then for an ultrafilter u on I. we have a closed subspace

. Using this, we construct ultraproducts in L

. Using the relationship between Nor

and L

and that between Nor

and Ba

, we show thatour ultraproducts in Nor

and Ba

are exactly those in the literatures. For the terminology, we refer to [6] for the category theory and to [8] for ultraproducts in Ba

..