Abstract This paper presents a formal model of concurrent processes whose functions can be modified from the environments during execution. In many applications, it takes too much cost to stop the whole of the concurrent system working in distributed environments to update its components. Features of dynamic evolution that make it possible to modify functions of processes without termination are important. In this paper, a formal model of evolvable concurrent processes is presented using logical formulas of linear logic. The operational semantics is defined using a formal proof in a fragment of the sequent calculus of linear logic. A method for replacing the continuations of working processes by applications of inference rules of linear logic is presented.