While there has been considerable research on the interactions between invasive and native species, and on the impact of invasive species on the resident community, there has been less focus on exploring the relationship and interactions among invasive species themselves. Nevertheless, it is widely recognised that invasive species can have either positive or negative effects on each other, as well as neutral outcomes. In the present theoretical study, we compared the success of two invasive non-native species in two scenarios: when they invaded the resident food web separately and simultaneously. We examined the correlations between their direct and indirect ecological relationships and their topological positions in the food web, with the varying outcomes of joint invasion. Using the Allometric Bioenergetic Model (ABM) for dynamic simulations, we determined the success of invasion (presence or absence of invaders) and, in the case of successful co-invasion, the direction of their biomass change, comparing separate and simultaneous invasion scenarios. We studied the relationships between these variables after detailed numerical simulations with variable key parameters of the model.We found that direct and indirect ecological relationships between the two invaders can significantly modifiy the outcomes of the invasion scenarios. For example, their predator-prey relationship increases the probability of invasion success for both invaders, but at the same time the equilibrium biomass of at least one of them is likely to be reduced compared to its separate invasion. Trophic cascade or competitive relationship between them during simultaneous invasion also affects their success rate, with the former having a positive effect and the latter a negative one, as they can hinder each other's spread. Further, we found that higher trophic level and lower betweenness centralities of the invaders reduces the likelihood of invasion success regardless of the presence or absence of another invasive species. The results of the study can be tested experimentally in micro- and mesocosms.