Abstract: In this paper,two form ulation theorems of time-differ encefidelity schemes for general quadratic and cubic physical conservation laws are respectively constructed and proved,withear lier major conserving time-discretized schemesgiven as special cases.These two theorems can provi denew mathem atical basis for solving basic formulation problem sofmore types of conservative time-discretef idelity schemes,and even for formulating conserv ative temporal-spatial discrete fidelity schemes by combining existing instantly conserving space-discretized schenes.Besides,the two theorems canalso solve two large categories of problems about linear and nonlinear computational instability.