diff --git a/lib/construct.c b/lib/construct.c
index 62bf32d..965beae 100644
--- a/lib/construct.c
+++ b/lib/construct.c
@@ -85,7 +85,103 @@ static void construct_sequence(const regex_sequence_t *seq, fsa_t *out)
 	assert(out->states[0].final);
 }
 
+static void retarget_merged_rules(
+    fsa_rule_t *rules, int rules_count, int initial, int base_initial,
+    int base_count)
+{
+	for (int i = 0; i < rules_count; ++i) {
+		if (0 == rules[i].next)
+			continue;
+
+		// IDs less than initial have to be offset by one less than
+		// base_count because the final state (ID zero) is not copied.
+		// If they are greater it's two less as the initial state is
+		// also not copied.  Finally, if the target is the initial
+		// state then it should be changed to the base's initial
+		// state.
+		if (rules[i].next < initial)
+			rules[i].next += base_count - 1;
+		else if (rules[i].next > initial)
+			rules[i].next += base_count - 2;
+		else
+			rules[i].next = base_initial;
+	}
+}
+
+static void merge_fsas(fsa_t *base, const fsa_t *other)
+{
+	const int new_count = base->count + other->count - 2;
+	if (base->capacity < new_count) {
+		do
+			base->capacity *= 2;
+		while (base->capacity < new_count);
+		base->states
+		    = realloc(base->states, base->capacity * sizeof(fsa_state_t));
+		assert(base->states);
+	}
+
+	// Copy rules from the other's initial state into the base's, then
+	// retarget them.
+	fsa_state_t *initial = &base->states[base->initial];
+	const fsa_state_t *other_initial = &other->states[other->initial];
+	const int new_rule_count = initial->count + other_initial->count;
+	if (initial->capacity < new_rule_count) {
+		do
+			initial->capacity *= 2;
+		while (initial->capacity < new_rule_count);
+		initial->rules = realloc(
+		    initial->rules, initial->capacity * sizeof(fsa_rule_t));
+		assert(initial->rules);
+	}
+	memcpy(
+	    &initial->rules[initial->count], other_initial->rules,
+	    other_initial->count * sizeof(fsa_rule_t));
+	retarget_merged_rules(
+	    &initial->rules[initial->count], other_initial->count,
+	    other->initial, base->initial, base->count);
+	initial->count = new_rule_count;
+
+	// Copy other states, skipping the initial state, then retarget
+	// their rules.
+	int offset = base->count;
+	if (1 < other->initial) {
+		const int copy_count = other->initial - 1;
+		const int copy_size = copy_count * sizeof(fsa_state_t);
+		memcpy(&base->states[offset], &other->states[1], copy_size);
+		offset += copy_count;
+	}
+	if (other->initial < other->count - 1) {
+		const int copy_count = other->count - other->initial - 1;
+		const int copy_size = copy_count * sizeof(fsa_state_t);
+		memcpy(
+		    &base->states[offset], &other->states[other->initial],
+		    copy_size);
+	}
+	for (int i = base->count; i < new_count; ++i) {
+		retarget_merged_rules(
+		    base->states[i].rules, base->states[i].count, other->initial,
+		    base->initial, base->count);
+	}
+	base->count = new_count;
+
+	free(other->states[0].rules);
+	free(other->states[other->initial].rules);
+	free(other->states);
+
+	assert(base->states[0].final);
+}
+
 void construct(const regex_t *regex, fsa_t *out)
 {
+	assert(regex->count > 0);
+
+	fsa_t sequence_fsa;
 	construct_sequence(&regex->contents[0], out);
+	for (int i = 1; i < regex->count; ++i) {
+		construct_sequence(&regex->contents[i], &sequence_fsa);
+		merge_fsas(out, &sequence_fsa);
+	}
+
+	assert(out->initial == out->count - 1);
+	assert(out->states[0].final);
 }
diff --git a/tests/construct_tests.c b/tests/construct_tests.c
index 83199a0..304cbc9 100644
--- a/tests/construct_tests.c
+++ b/tests/construct_tests.c
@@ -102,11 +102,42 @@ static void test_sequence(void)
 	fsa_free(&fsa);
 }
 
+static void test_union(void)
+{
+	const char *literals = "abc";
+	regex_sequence_t *alternatives = malloc(3 * sizeof(regex_sequence_t));
+	for (int i = 0; i < 3; ++i) {
+		regex_term_t *terms = malloc(1 * sizeof(regex_term_t));
+		terms[0].quantifier = REGEX_QUANTIFIER_NONE;
+		terms[0].type = REGEX_TERM_LITERAL;
+		terms[0].literal = literals[i];
+
+		alternatives[i].count = alternatives[i].capacity = 1;
+		alternatives[i].contents = terms;
+	}
+	regex_t regex = { .count = 3, .capacity = 3, .contents = alternatives };
+
+	fsa_t fsa;
+	construct(&regex, &fsa);
+
+	const fsa_state_t *initial = &fsa.states[fsa.initial];
+	ASSERT_EQ(3, initial->count);
+	for (int i = 0; i < 3; ++i) {
+		ASSERT_EQ(literals[i], initial->rules[i].input);
+		const int next = initial->rules[i].next;
+		ASSERT_TRUE(fsa.states[next].final);
+	}
+
+	regex_free(&regex);
+	fsa_free(&fsa);
+}
+
 int main(void)
 {
 	TESTING_BEGIN();
 	test_empty_expression();
 	test_literal_expression();
 	test_sequence();
+	test_union();
 	return TESTING_END();
 }