  We reconstruct Peleg's concurrent dynamic logic in the context of modal
Kleene algebras. We explore the algebraic structure of its multirelational
semantics and develop an abstract axiomatisation of concurrent dynamic algebras
from that basis. In this axiomatisation, sequential composition is not
associative. It interacts with concurrent composition through a weak
distributivity law. The modal operators of concurrent dynamic algebra are
obtained from abstract axioms for domain and antidomain operators; the Kleene
star is modelled as a least fixpoint. Algebraic variants of Peleg's axioms are
shown to be valid in these algebras and their soundness is proved relative to
the multirelational model. Additional results include iteration principles for
the Kleene star and a refutation of variants of Segerberg's axiom in the
multirelational setting. The most important results have been verified formally
with Isabelle/HOL.
