This paper presents two related algebras which can be used to specify and analyse concurrent systems with synchronous and asynchronous communications. The first algebra is based on a class of P/T-nets, called boxes, and their standard transition firing rule. It is an extension of the Petri Box Calculus (PBC). Essentially, the original model is enriched with the introduction of special buffer places where different transitions (processes) may deposit and remove tokens, together with an explicit asynchronous communication operator, denoted by tie, allowing to make them private. We also introduce an algebra of process expressions corresponding to such a net algebra, by augmenting the existing syntax of PBC expressions, and defining a system of SOS rules providing their operational semantics. The two algebras are related through a mapping which, for any extended box expression, returns a corresponding box with an isomorphic transition system.