diff --git a/.github/workflows/gha_ci.yml b/.github/workflows/gha_ci.yml
index 3ea2d68ca..70a4714bc 100644
--- a/.github/workflows/gha_ci.yml
+++ b/.github/workflows/gha_ci.yml
@@ -81,6 +81,12 @@ jobs:
       - uses: actions/checkout@v4
       - name: Build
         run: bash tools/gha_conda_ubsan.sh
+  conda_llvm18_asan:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - name: Build
+        run: bash tools/gha_llvm18_conda_asan.sh
   conda_llvm17_asan:
     runs-on: ubuntu-latest
     steps:
diff --git a/CMakeLists.txt b/CMakeLists.txt
index 6cfdd07bf..9d2c8cb77 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -158,8 +158,8 @@ endif()
 include(GNUInstallDirs)
 find_package(LLVM REQUIRED CONFIG)
 
-if(${LLVM_VERSION_MAJOR} LESS 15 OR ${LLVM_VERSION_MAJOR} GREATER 18)
-  message(FATAL_ERROR "LLVM >= 15 and <= 18 is required.")
+if(${LLVM_VERSION_MAJOR} LESS 15 OR ${LLVM_VERSION_MAJOR} GREATER 19)
+  message(FATAL_ERROR "LLVM >= 15 and <= 19 is required.")
 endif()
 
 # List of source files.
diff --git a/doc/changelog.rst b/doc/changelog.rst
index fd558726f..2eea22c2f 100644
--- a/doc/changelog.rst
+++ b/doc/changelog.rst
@@ -7,6 +7,7 @@ Changelog
 New
 ~~~
 
+- Support LLVM 19 (`#455 <https://github.com/bluescarni/heyoka/pull/455>`__).
 - Non-number exponents for the ``pow()`` function
   are now supported in Taylor integrators
   (`#454 <https://github.com/bluescarni/heyoka/pull/454>`__).
diff --git a/doc/install.rst b/doc/install.rst
index cad4aeac9..c80b936b8 100644
--- a/doc/install.rst
+++ b/doc/install.rst
@@ -14,7 +14,7 @@ and several CPU architectures (x86-64, 64-bit ARM and 64-bit PowerPC).
 
 heyoka has the following **mandatory** dependencies:
 
-* the `LLVM <https://llvm.org/>`__ compiler infrastructure library (version >=15 and <=18),
+* the `LLVM <https://llvm.org/>`__ compiler infrastructure library (version >=15 and <=19),
 * the `Boost <https://www.boost.org/>`__ C++ libraries (version >=1.69),
 * the `{fmt} <https://fmt.dev/latest/index.html>`__ library (version >=9 and <=11),
 * the `spdlog <https://github.com/gabime/spdlog>`__ library,
diff --git a/tools/gha_conda_clang_tidy.sh b/tools/gha_conda_clang_tidy.sh
old mode 100755
new mode 100644
diff --git a/tools/gha_conda_ubsan.sh b/tools/gha_conda_ubsan.sh
old mode 100755
new mode 100644
diff --git a/tools/gha_llvm16_conda_asan.sh b/tools/gha_llvm16_conda_asan.sh
old mode 100755
new mode 100644
diff --git a/tools/gha_llvm17_conda_asan.sh b/tools/gha_llvm17_conda_asan.sh
old mode 100755
new mode 100644
diff --git a/tools/gha_llvm18_conda_asan.sh b/tools/gha_llvm18_conda_asan.sh
new file mode 100644
index 000000000..ab0b6137a
--- /dev/null
+++ b/tools/gha_llvm18_conda_asan.sh
@@ -0,0 +1,48 @@
+#!/usr/bin/env bash
+
+# Echo each command
+set -x
+
+# Exit on error.
+set -e
+
+# Core deps.
+sudo apt-get install wget
+
+# Install conda+deps.
+wget https://github.com/conda-forge/miniforge/releases/latest/download/Miniforge3-Linux-x86_64.sh -O miniconda.sh
+export deps_dir=$HOME/local
+export PATH="$HOME/miniconda/bin:$PATH"
+bash miniconda.sh -b -p $HOME/miniconda
+conda create -y -p $deps_dir c-compiler cxx-compiler cmake ninja 'llvmdev=18.*' \
+    tbb-devel tbb libboost-devel 'mppp=1.*' sleef xtensor xtensor-blas blas \
+    blas-devel fmt spdlog
+source activate $deps_dir
+
+# Create the build dir and cd into it.
+mkdir build
+cd build
+
+# Clear the compilation flags set up by conda.
+unset CXXFLAGS
+unset CFLAGS
+
+# Configure.
+cmake ../ -G Ninja \
+    -DCMAKE_PREFIX_PATH=$deps_dir \
+    -DCMAKE_BUILD_TYPE=Debug \
+    -DHEYOKA_BUILD_TESTS=yes \
+    -DHEYOKA_BUILD_TUTORIALS=ON \
+    -DHEYOKA_WITH_MPPP=yes \
+    -DHEYOKA_WITH_SLEEF=yes \
+    -DCMAKE_CXX_FLAGS="-fsanitize=address" \
+    -DCMAKE_CXX_FLAGS_DEBUG="-g -Og"
+
+# Build.
+ninja -v
+
+# Run the tests.
+ctest -VV -j4
+
+set +e
+set +x