diff --git a/lmformatenforcer/__init__.py b/lmformatenforcer/__init__.py
index 85510e7..5d3bfce 100644
--- a/lmformatenforcer/__init__.py
+++ b/lmformatenforcer/__init__.py
@@ -1,12 +1,14 @@
 __all__ = ['CharacterLevelParser', 
            'StringParser', 
            'RegexParser', 
+           'UnionParser',
+           'SequenceParser',
            'JsonSchemaParser',
            'TokenEnforcer', 
            'LMFormatEnforcerException',
            'FormatEnforcerAnalyzer',]
 
-from .characterlevelparser import CharacterLevelParser, StringParser
+from .characterlevelparser import CharacterLevelParser, StringParser, UnionParser, SequenceParser
 from .regexparser import RegexParser
 from .jsonschemaparser import JsonSchemaParser
 from .tokenenforcer import TokenEnforcer
diff --git a/lmformatenforcer/characterlevelparser.py b/lmformatenforcer/characterlevelparser.py
index ccc2d53..939d8be 100644
--- a/lmformatenforcer/characterlevelparser.py
+++ b/lmformatenforcer/characterlevelparser.py
@@ -1,5 +1,5 @@
 import abc
-from typing import Hashable, Optional
+from typing import Hashable, List, Optional
 
 
 class CharacterLevelParser(abc.ABC):
@@ -11,7 +11,7 @@ def add_character(self, new_character: str) -> 'CharacterLevelParser':
         raise NotImplementedError()
 
     @abc.abstractmethod
-    def get_allowed_characters(self) ->str:
+    def get_allowed_characters(self) -> str:
         """Return a string containing all characters that are allowed at the current point in the parsing process."""
         raise NotImplementedError()
     
@@ -56,3 +56,77 @@ def get_allowed_characters(self) -> str:
         return ""
     def can_end(self) -> bool:
         return True
+    
+
+class UnionParser(CharacterLevelParser):
+    """A parser that allows a string that would be allowed by any of several different parsers"""
+    def __init__(self, parsers: List[CharacterLevelParser]):
+        self.parsers = parsers
+
+    def add_character(self, new_character: str) -> CharacterLevelParser:
+        # This is a bit of a performance hit, as it means get_allowed_characters() is called twice.
+        relevant_parsers = [parser for parser in self.parsers if new_character in parser.get_allowed_characters()]
+        next_parsers = [parser.add_character(new_character) for parser in relevant_parsers]
+        if len(next_parsers) == 1:
+            return next_parsers[0]
+        return UnionParser(next_parsers)
+    
+    def get_allowed_characters(self) -> str:
+        allowed = "".join([parser.get_allowed_characters() for parser in self.parsers])
+        return "".join(set(allowed))
+    
+    def can_end(self) -> bool:
+        return any([parser.can_end() for parser in self.parsers])
+    
+    def shortcut_key(self) -> str | None:
+        return self.parsers[0].shortcut_key() if len(self.parsers) == 1 else None
+    
+    def cache_key(self) -> Optional[Hashable]:
+        all_cache_keys = tuple(parser.cache_key() for parser in self.parsers)
+        if all(key is not None for key in all_cache_keys):
+            return ('union', all_cache_keys)
+        return None
+
+
+class SequenceParser(CharacterLevelParser):
+    """A parser that is a sequence of multiple parsers."""
+    def __init__(self, parsers: List[CharacterLevelParser]):
+        self.parsers = parsers
+
+    def add_character(self, new_character: str) -> CharacterLevelParser:
+        legal_parsers = []
+        # Tricky edge case: if the first parser can both end and accept the character,
+        # and the second parser can also accept, we don't know which scenario we are dealing
+        # with, so we need to return a UnionParser.
+        for idx, parser in enumerate(self.parsers):
+            if new_character in parser.get_allowed_characters():
+                updated_parser = parser.add_character(new_character)
+                next_parsers = [updated_parser] + self.parsers[idx+1:]
+                legal_parsers.append(SequenceParser(next_parsers))
+            if not parser.can_end():
+                break
+        if len(legal_parsers) == 1:
+            return legal_parsers[0]
+        return UnionParser(legal_parsers)
+    
+    def get_allowed_characters(self) -> str:
+        allowed_character_strs = []
+        for parser in self.parsers:
+            allowed_character_strs.append(parser.get_allowed_characters())
+            if not parser.can_end():
+                break
+        return "".join([parser.get_allowed_characters() for parser in self.parsers])
+    
+    def can_end(self) -> bool:
+        return all([parser.can_end() for parser in self.parsers])
+    
+    def shortcut_key(self) -> Optional[str]:
+        return self.parsers[0].shortcut_key() if len(self.parsers) == 1 else None
+    
+    def cache_key(self) -> Optional[Hashable]:
+        all_cache_keys = tuple(parser.cache_key() for parser in self.parsers)
+        if all(key is not None for key in all_cache_keys):
+            return ('sequence', all_cache_keys)
+        return None
+
+
diff --git a/tests/test_composite_parsers.py b/tests/test_composite_parsers.py
new file mode 100644
index 0000000..2bfc9f1
--- /dev/null
+++ b/tests/test_composite_parsers.py
@@ -0,0 +1,31 @@
+from lmformatenforcer import UnionParser, SequenceParser, StringParser
+from .common import assert_parser_with_string
+from pydantic import BaseModel
+from lmformatenforcer import JsonSchemaParser
+
+
+def test_string_choice():
+    parser = UnionParser([StringParser('aa'), StringParser('bb')])
+    assert_parser_with_string('aa', parser, True)
+    assert_parser_with_string('bb', parser, True)
+    assert_parser_with_string('ab', parser, False)
+    assert_parser_with_string('aabb', parser, False)
+
+
+def test_string_sequence():
+    parser  = SequenceParser([StringParser('aa'), StringParser('bb')])
+    assert_parser_with_string('aa', parser, False)
+    assert_parser_with_string('bb', parser, False)
+    assert_parser_with_string('ab', parser, False)
+    assert_parser_with_string('aabb', parser, True)
+    assert_parser_with_string('bbaa', parser, False)
+
+
+def test_json_markdown_sequence():
+    class TestModel(BaseModel):
+        a: str
+    json_parser = JsonSchemaParser(TestModel.schema())
+    parser = SequenceParser([StringParser("```json\n"), json_parser, StringParser('\n```')])
+    assert_parser_with_string('```json\n{"a": "b"}\n```', parser, True)
+    assert_parser_with_string('{"a": "b"}', parser, False)
+
diff --git a/tests/test_jsonschemaparser.py b/tests/test_jsonschemaparser.py
index 160b513..f1f824a 100644
--- a/tests/test_jsonschemaparser.py
+++ b/tests/test_jsonschemaparser.py
@@ -1,6 +1,6 @@
 import json
 from typing import Dict, List, Optional
-from pydantic import BaseModel, Field, conlist
+from pydantic import BaseModel, Field
 from lmformatenforcer import JsonSchemaParser
 from enum import Enum
 import pytest