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Let $A$ and $B$ be two stably projectionless separable simple amenable C*-algebras with $gTR(A)\\le 1$and $gTR(B)\\le 1.$ Suppose also that $KK(A, D)=KK(B,D)=\\{0\\}$ for all C*-algebras $D.$ Then $A\\cong B$ if and only if they have the same tracial cones with scales. We also show that every separable simple C*-algebra, $A$ with finite nuclear dimension which satisfies the UCT with non-zero traces must have $gTR(A)\\le 1$ if $K_0(A)$ is torsion. 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Generalized tracial rank one is defined for stably projectionless simple C*-algebras. Let $A$ and $B$ be two stably projectionless separable simple amenable C*-algebras with $gTR(A)\\le 1$and $gTR(B)\\le 1.$ Suppose also that $KK(A, D)=KK(B,D)=\\{0\\}$ for all C*-algebras $D.$ Then $A\\cong B$ if and only if they have the same tracial cones with scales. We also show that every separable simple C*-algebra, $A$ with finite nuclear dimension which satisfies the UCT with non-zero traces must have $gTR(A)\\le 1$ if $K_0(A)$ is torsion. 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