Semistructured data is not strictly typed like relational or object-oriented data and may be irregular or incomplete. It often arises in practice, e.g., when heterogeneous data sources are integrated or data is taken from the World Wide Web. Views over semistructured data can be used to filter the data and to restructure (or provide structure to) it. To achieve fast query response time, these views are often materialized. This paper studies incremental maintenance techniques for materialized views over semistructured data. We use the graph-based data model OEM and the query language Lorel, developed at Stanford, as the framework for our work. We propose a new algorithm that produces a set of queries that compute the changes to the view based upon a change to the source. We develop an analytic cost model and compare the cost of executing our incremental maintenance algorithm to that of recomputing the view. We show that for nearly all types of database updates, it is more efficient to apply our incremental maintenance algorithm to the view than to recompute the view from the database, even when there are thousands of such updates.