A rule \phi_1, ..., \phi_k / \psi is admissible in a (nonclassical) propositional logic L if the set of L-tautologies is closed under substitution instances of the rule. We are particularly interested in the set-up with parameters (constants), which are required to be preserved by substitutions. In this talk, we shall study basic properties of admissibility with parameters in a class of well-behaved transitive modal logics (i.e., extensions of K4). The main goal is a classification of the computational complexity of admissibility (and the closely related problem of unifiability) with parameters based on semantic properties of logics.