diff --git a/src/test/fuzz/CMakeLists.txt b/src/test/fuzz/CMakeLists.txt
--- a/src/test/fuzz/CMakeLists.txt
+++ b/src/test/fuzz/CMakeLists.txt
@@ -112,6 +112,7 @@
 	parse_univalue
 	prevector
 	pow
+	primitives_transaction
 	process_message
 	process_messages
 	protocol
diff --git a/src/test/fuzz/block.cpp b/src/test/fuzz/block.cpp
--- a/src/test/fuzz/block.cpp
+++ b/src/test/fuzz/block.cpp
@@ -63,4 +63,9 @@
     (void)block.GetHash();
     (void)block.ToString();
     (void)BlockMerkleRoot(block);
+
+    CBlock block_copy = block;
+    block_copy.SetNull();
+    const bool is_null = block_copy.IsNull();
+    assert(is_null);
 }
diff --git a/src/test/fuzz/primitives_transaction.cpp b/src/test/fuzz/primitives_transaction.cpp
new file mode 100644
--- /dev/null
+++ b/src/test/fuzz/primitives_transaction.cpp
@@ -0,0 +1,39 @@
+// Copyright (c) 2020 The Bitcoin Core developers
+// Distributed under the MIT software license, see the accompanying
+// file COPYING or http://www.opensource.org/licenses/mit-license.php.
+
+#include <primitives/transaction.h>
+
+#include <test/fuzz/FuzzedDataProvider.h>
+#include <test/fuzz/fuzz.h>
+#include <test/fuzz/util.h>
+
+#include <cstdint>
+#include <optional>
+#include <string>
+#include <vector>
+
+void test_one_input(const std::vector<uint8_t> &buffer) {
+    FuzzedDataProvider fuzzed_data_provider(buffer.data(), buffer.size());
+    const CScript script = ConsumeScript(fuzzed_data_provider);
+    const std::optional<COutPoint> out_point =
+        ConsumeDeserializable<COutPoint>(fuzzed_data_provider);
+    if (out_point) {
+        const CTxIn tx_in{*out_point, script,
+                          fuzzed_data_provider.ConsumeIntegral<uint32_t>()};
+        (void)tx_in;
+    }
+    const CTxOut tx_out_1{ConsumeMoney(fuzzed_data_provider), script};
+    const CTxOut tx_out_2{ConsumeMoney(fuzzed_data_provider),
+                          ConsumeScript(fuzzed_data_provider)};
+    assert((tx_out_1 == tx_out_2) != (tx_out_1 != tx_out_2));
+    const std::optional<CMutableTransaction> mutable_tx_1 =
+        ConsumeDeserializable<CMutableTransaction>(fuzzed_data_provider);
+    const std::optional<CMutableTransaction> mutable_tx_2 =
+        ConsumeDeserializable<CMutableTransaction>(fuzzed_data_provider);
+    if (mutable_tx_1 && mutable_tx_2) {
+        const CTransaction tx_1{*mutable_tx_1};
+        const CTransaction tx_2{*mutable_tx_2};
+        assert((tx_1 == tx_2) != (tx_1 != tx_2));
+    }
+}