The deformation complex of an algebra over a colored PROP P is defined in terms of a minimal (or, more generally, cofibrant) model of P. It is shown that it carries the structure of an L_∞-algebra which induces a graded Lie bracket on cohomology.

As an example, the L_∞-algebra structure on the deformation complex of an associative algebra morphism g is constructed. Another example is the deformation complex of a Lie algebra morphism. The last example is the diagram describing two mutually inverse morphisms of vector spaces. Its L_∞-deformation complex has nontrivial l₀-term.

Explicit formulas for the L_∞-operations in the above examples are given. A typical deformation complex of a diagram of algebras is a fully-fledged L_∞-algebra with nontrivial higher operations.

The first author worked in the frame of grant F1R-MTH-PUL-08GEOQ of Professor Schlichenmaier. The second author was supported by the grant GA ČR 201/08/0397 and by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AV0Z10190503.