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In this paper, we present Local Church\u2013Rosser, Parallelism, Concurrency and Amalgamation Theorems for rules with nested application conditions in the framework of<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0960129512000357_inline2\"\/><jats:tex-math>$\\mathcal{M}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-adhesive categories, where<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0960129512000357_inline2\"\/><jats:tex-math>$\\mathcal{M}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-adhesive categories are slightly more general than weak adhesive high-level replacement categories. Most of the proofs are based on the corresponding statements for rules without application conditions and two shift lemmas stating that nested application conditions can be shifted over morphisms and rules.<\/jats:p>","DOI":"10.1017\/s0960129512000357","type":"journal-article","created":{"date-parts":[[2014,6,26]],"date-time":"2014-06-26T14:22:13Z","timestamp":1403792533000},"source":"Crossref","is-referenced-by-count":46,"title":["-adhesive transformation systems with nested application conditions. Part 1: parallelism, concurrency and amalgamation"],"prefix":"10.1017","volume":"24","author":[{"given":"HARTMUT","family":"EHRIG","sequence":"first","affiliation":[]},{"given":"ULRIKE","family":"GOLAS","sequence":"additional","affiliation":[]},{"given":"ANNEGRET","family":"HABEL","sequence":"additional","affiliation":[]},{"given":"LEEN","family":"LAMBERS","sequence":"additional","affiliation":[]},{"given":"FERNANDO","family":"OREJAS","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,6,26]]},"reference":[{"key":"S0960129512000357_ref32","volume-title":"Handbook of Graph Grammars and Computing by Graph Transformation 3: Concurrency, Parallelism, and Distribution","author":"Ehrig","year":"1999"},{"key":"S0960129512000357_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-53982-4_16"},{"key":"S0960129512000357_ref26","doi-asserted-by":"crossref","first-page":"35","DOI":"10.3233\/FI-2012-705","article-title":"$\\mathcal{M}$-Adhesive Transformation Systems with Nested Application Conditions. 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