Clinical guidelines are intended to improve the quality and cost effectiveness of patient care. Integration of guidelines into electronic medical records and order-entry systems, in a way that enables delivery of patient-specific advice at the point of care, is likely to encourage guidelines acceptance and effectiveness. Among the methodologies for modeling guidelines and medical decision rules, the Arden Syntax for Medical Logic Modules and the GuideLine Interchange Format version 3 (GLIF3) emphasize the importance of sharing encoded logic across different medical institutions and implementation platforms. These two methodologies have similarities and differences; in this paper we clarify their roles. Both methods can be used to support sharing of medical knowledge, but they do so in complementary situations. The Arden Syntax is suitable for representing individual decision rules in self-contained units called Medical Logic Modules (MLMs), which are usually implemented as event-driven alerts or reminders. In contrast, GLIF3 is designed for encoding complex multistep guidelines that unfold over time. As a consequence, GLIF3 has several mechanisms for complexity management and additional constructs that may require overhead unnecessary for expressing simple alerts and reminders. Unlike the Arden Syntax, GLIF3 encourages a top-down process of guideline modeling consisting of three levels that are created in order: Level 1 comprises a human-readable flowchart of clinical decisions and actions. Level 2 comprises a computable specification that can be verified for logical consistency and completeness; and Level 3 comprises an implementable specification that includes information required for local adaptation of guideline logic as well as for mapping guideline variables onto institutional medical records. A major emphasis of the current GLIF3 development process has been to create the computable specification that formally represents medical decision and eligibility criteria. We based GLIF3's formal expression language on the Arden Syntax's logic grammar, making the necessary extensions to the Arden Syntax's data structures and operators to support GLIF3's object-oriented data model. We discuss why the process of generating a set of MLMs from a GLIF-encoded guideline cannot be automated, why it can result in information loss, and why simple medical rules are best represented as individual MLMs. We thus show that the Arden Syntax and GLIF3 play complementary roles in representing medical knowledge for clinical decision support.