NOVELTY - A recombinant host cell (D1) with elevated expression or activity of the following enzymes as compared to the parent host cell it is derived from 4-hydroxybutyryl-CoA dehydratase; and crotonate CoA-transferase, and/or at least one, preferably all of the enzymes (A1) of at least one of (i) 2-ketoacid decarboxylase, (ii) 2-ketoglutarate dehydrogenase, succinyl-CoA synthetase and succinic semialdehyde dehydrogenase, (iii) 2-ketoglutarate dehydrogenase and succinyl-CoA reductase, and (iv) glutamate dehydrogenase, glutamate decarboxylase and gamma -amino-N-butyrate transaminase, is new.    USE - For the production of compound selected from crotonic acid, crotonyl-CoA, butyryl-CoA, butyric acid, butyraldehyde and butanol; and for the production of fuel (claimed).    ADVANTAGE - The host cell shows natural and/or enhanced recombinant activity of 3-hydroxypropionate/4-hydroxybutyrate cycle or its parts.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the followings:    (1) new host cell (D2) engineered with nucleic acids encoding the enzyme of 4-hydroxybutyryl-CoA dehydratase, and crotonate CoA-transferase, and/or the enzymes (A1);    (2) producing a compound selected from crotonic acid, crotonyl-CoA, butyryl-CoA, butyric acid, butyraldehyde and butanol, involving culturing a host cell (D3) to produce the compound, where the host cell (D3) uses glycerol, polysaccharides, oligosaccharides, sugar, alcohols, polyalcohols, glycerol, fatty acids, proteins, amino acids and/or lipid as carbon source, and where the host cell (D3) is selected from the recombinant or engineered host cell (D1) or (D2), a host cell with elevated expression or activity of at least one enzyme (A1) as compared to the parent host cell it is derived from, and a host cell engineered with nucleic acid encoding at least one enzyme (A1);    (3) use of a host cell (D3) for the production of a compound selected from crotonic acid, crotonyl-CoA, butyryl-CoA, butyric acid, butyraldehyde and butanol;    (4) a kit containing nucleic acid encoding 4-hydroxybutyryl-CoA dehydratase, and crotonate CoA-transferase and/or the enzyme (A1).