Summary: We derive local boundedness estimates for weak solutions of a large class of second-order quasilinear equations. The structural assumptions imposed on an equation in the class allow vanishing of the quadratic form associated with its principal part and require no smoothness of its coefficients. The class includes second-order linear elliptic equations as studied in [D. Gilbarg and N. S. Trudinger, “Elliptic partial differential equations of second order. Reprint of the 1998 ed.”, Classics in Mathematics. Berlin: Springer,(2001; Zbl 1042.35002)] and second-order subelliptic linear equations as in the papers of E. T. Sawyer and {R. L. Wheeden} [Mem. Am. Math. Soc. 847, 157 p. (2006; Zbl 1096.35031)], [Trans. Am. Math. Soc. 362, No. 4, 1869–1906 (2010; Zbl 1191.35085)]. Our results also extend ones obtained by J. Serrin [Acta Math. 111, 247–302 (1964; Zbl 0128.09101)] concerning local boundedness of weak solutions of quasilinear elliptic equations.