Drilling and completion muds useful at elevated temperatures

A clay based aqueous drilling or completion mud comprising clay, density increasing material, viscosity increasing agent, and from 1 to 10 grams per liter of a hydrosoluble polymeric material having pendant groups and a weight average molecular weight not higher than about 40,000, wherein from about 2 to 95% of the pendant groups are independently hydroxamic or thiohydroxamic groups of the formula:

• ##STR7## wherein X.sub.1 and X.sub.2 are independently oxygen, or sulfur and R and R' are independently hydrogen, alkyl or cycloalkyl having from 1 to about 18 carbon atoms, alkylene and cycloalkylene having from about 2 to 18 carbon atoms, aryl, alkylaryl, arylalkyl, alkoxyaryl, and alkoxyalkyl, having up to two conjugated rings, and having up to about 18 carbon atoms and wherein said polymeric material before the introduction of the hydroxamic or thiohydroxamic groups, is a homopolymer of acrylamide, methacrylamide, alkylacrylamide, thioacrylamide, alkylthioacrylamide, and hydroxyalkylacrylates, or copolymers of a monomer selected from acrylamide, methacrylamide, alklyacrylamide, thioacrylamide, alkylthioacrylamide, and hydroxyalkylacrylates and a monomer selected from acrylic acid, alkylacrylic acid, salts of acrylic acid and alkylacrylic acid, esters of acrylic acid and alkylacrylic acid, maleicanhydride, vinylacetate, vinyl pyrrolidone, butadiene, styrene and acrylonitrile.