diff --git a/test/crypto/eax.js b/test/crypto/eax.js
index b7280b04..d46fa57a 100644
--- a/test/crypto/eax.js
+++ b/test/crypto/eax.js
@@ -125,6 +125,7 @@ function testAESEAX() {
   });
 }
 
+/* eslint-disable no-invalid-this */
 module.exports = () => describe('Symmetric AES-EAX', function() {
   let sinonSandbox;
   let getWebCryptoStub;
@@ -142,6 +143,11 @@ module.exports = () => describe('Symmetric AES-EAX', function() {
   };
 
   describe('Symmetric AES-EAX (native)', function() {
+    before(function () {
+      const detectNative = () => !!(util.getWebCrypto() || util.getNodeCrypto());
+      if (!detectNative()) { this.skip(); }
+    });
+
     beforeEach(function () {
       sinonSandbox = sandbox.create();
       enableNative();
diff --git a/test/crypto/rsa.js b/test/crypto/rsa.js
index bc2e81c9..daae61a6 100644
--- a/test/crypto/rsa.js
+++ b/test/crypto/rsa.js
@@ -25,6 +25,8 @@ module.exports = () => describe('basic RSA cryptography', function () {
     sinonSandbox.restore();
   });
 
+  const detectNative = () => !!(util.getWebCrypto() || util.getNodeCrypto());
+
   const disableNative = () => {
     enableNative();
     // stubbed functions return undefined
@@ -105,6 +107,8 @@ module.exports = () => describe('basic RSA cryptography', function () {
   });
 
   it('compare native crypto and bnSign', async function() {
+    if (!detectNative()) { this.skip(); }
+
     const bits = 1024;
     const { publicParams, privateParams } = await crypto.generateParams(openpgp.enums.publicKey.rsaSign, bits);
     const { n, e, d, p, q, u } = { ...publicParams, ...privateParams };
@@ -120,6 +124,8 @@ module.exports = () => describe('basic RSA cryptography', function () {
   });
 
   it('compare native crypto and bnVerify', async function() {
+    if (!detectNative()) { this.skip(); }
+
     const bits = 1024;
     const { publicParams, privateParams } = await crypto.generateParams(openpgp.enums.publicKey.rsaSign, bits);
     const { n, e, d, p, q, u } = { ...publicParams, ...privateParams };