diff --git a/pyproject.toml b/pyproject.toml
index c07091d..156f7d4 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -11,7 +11,7 @@ packages = [
 
 [tool.poetry.dependencies]
 python = "^3.7"
-tornado = "^6"
+tornado = "^4 || ^5 || ^6"
 openapi-core = "^0.13.4"
 
 [tool.poetry.dev-dependencies]
diff --git a/tox.ini b/tox.ini
new file mode 100644
index 0000000..b519bb9
--- /dev/null
+++ b/tox.ini
@@ -0,0 +1,17 @@
+[tox]
+isolated_build=true
+envlist = {py37,py38}-tornado{4,5,6}
+
+[testenv]
+deps =
+    tornado4: tornado>=4,<5
+    tornado5: tornado>=5,<6
+    tornado6: tornado>=6,<7
+    mypy
+    hypothesis
+    flake8
+    pytest
+    pytest-flake8
+    pytest-mypy
+whitelist_externals = poetry
+commands = py.test