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In this work, we study dynamic properties of classical solutions to ahomogenous Neumann initial-boundary value problem (IBVP) for a two-species andtwo-stimuli chemotaxis model with/without chemical signalling loop in a 2Dbounded and smooth domain. We successfully detect the product of two speciesmasses as a feature to determine boundedness, gradient estimates, blow-up and$W^{j,\infty}(1\leq j\leq 3)$-exponential convergence of classical solutionsfor the corresponding IBVP. More specifically, we first show generally asmallness on the product of both species masses, thus allowing one species massto be suitably large, is sufficient to guarantee global boundedness, higherorder gradient estimates and $W^{j,\infty}$-convergence with rates ofconvergence to constant equilibria; and then, in a special case, we detect astraight line of masses on which blow-up occurs for large product of masses.Our findings provide new understandings about the underlying model, and thus,improve and extend greatly the existing knowledge relevant to this model.

On boundedness, gradient estimate, blow-up and convergence in a two-species and two-stimuli chemotaxis system with/without loop