Summary: This paper studies necessity of transversality conditions for a continuous-time, reduced-form model. By generalizing Benveniste and Scheinkman’s (1982) ‘envelope’ condition and the version of the squeezing argument by P. G. Michel [Econometrica 58, No. 3, 705-723 (1990; Zbl 0731.90022)], we show a generalization of Michel’s necessity result [op. cit.] that does not assume concavity. The generalization enables us to generalize Ekeland and Scheinkman’s (1986) result as well as to establish a new result that does not require the objective functional to be finite. The new result implies that homogeneity of the return function alone is sufficient for the necessity of the most standard transversality condition. Our results are also applied to a nonstationary version of the one-sector growth model. It is shown that bubbles never arise in an equilibrium asset pricing model with a nonlinear constraint.