There is growing interest in promoting interoperability among the many different existent Grid initiatives. The requirements for interlinking of Grids have already been studied from a general point of view. In this paper, we analyse current practice in Grid interactions and show evidence of how Grid interactions may represent a barrier for interlinking of Grids. Our proposal consists of three combined aspects: a) explicitly modelling the interactions (what we call interaction protocols), b) decoupling the execution flow of services from their interactions with other services and c) services have to be able to dynamically select the interaction protocol at the time they have decided to interact with another party. Next, for a clarifying purpose, we show how DVega, an application built on the proposed principles, can use these features as the foundations for interacting with disparate services from different Grids in a flexible and dynamic way.