  In this article we classify indecomposable objects of the derived categories
of finitely-generated modules over certain infinite-dimensional algebras. The
considered class of algebras (which we call nodal algebras) contains such
well-known algebras as the complete ring of a double nodal point
$\kk[[x,y]]/(xy)$ and the completed path algebra of the Gelfand quiver. As a
corollary we obtain a description of the derived category of Harish-Chandra
modules over $SL_{2}({\mathbb R})$. We also give an algorithm, which allows to
construct projective resolutions of indecomposable complexes. In the appendix
we prove the Krull-Schmidt theorem for homotopy categories.
