Positive solutions are established for the singular second-order boundary value problem y " + phi(t)f(t, y, y') = 0, 0 < t < 1 y(0) = y'(1) = 0. Singularities at (i) y = 0 and y' = 0, (ii) y = 0 but not y' = 0, and (iii) y' = 0 but not y = 0 are discussed separately. (C) 1998 Academic Press.