In this paper we consider the problem of verification of large dynamic models of biological systems. We present syntactical criteria based on biochemical kinetics to ensure the plausibility of a model and the positivity of its solution. These criteria include the positivity of the rate functions, their kinetic type dependence on the reactant species concentrations, and the absence of the negative cross-effects that together guarantee the nonnegativity of the dynamics. Further, the stoichiometric matrix of the truncated reaction system is checked against conservation using its algebraic properties. Algorithmic procedures are then proposed for checking these criteria with emphasis on good scaling up properties. In addition to these verification procedures, we also provide, for certain typical errors, model correcting methods. The capabilities and usefulness of these procedures are illustrated on biochemical models taken from the Biomodels database. In particular, a set of 11 kinetic models related with E. coli are checked, finding two with deficiencies. Correcting actions for these models are proposed.