We investigate parametric polymorphism in message-based concurrent programming, focusing on behavioral equivalences in a typed process calculus analogous to the polymorphic λ- calculus of Girard and Reynolds. Polymorphism constrains the power of observers by preventing them from directly manipulating data values whose types are abstract, leading to notions of equivalence much coarser than the standard untied ones. We study the nature of these constraints through simple examples of concurrent abstract data types and develop basic theoretical machinery for establishing bisimilarity of polymorphic processes. We also observe some surprising interactions between polymorphism and aliasing, drawing examples from both the polymorphic π-calculus and ML.