diff --git a/classes/range.js b/classes/range.js
index 766d505a..a7d6556f 100644
--- a/classes/range.js
+++ b/classes/range.js
@@ -299,6 +299,10 @@ const replaceTildes = (comp, options) => {
 
 const replaceTilde = (comp, options) => {
   const r = options.loose ? re[t.TILDELOOSE] : re[t.TILDE]
+  // if we're including prereleases in the match, then the lower bound is
+  // -0, the lowest possible prerelease value, just like x-ranges and carets.
+  // this keeps `~1.2` equivalent to the `1.2.x` x-range it's documented as.
+  const z = options.includePrerelease ? '-0' : ''
   return comp.replace(r, (_, M, m, p, pr) => {
     debug('tilde', comp, _, M, m, p, pr)
     let ret
@@ -306,10 +310,10 @@ const replaceTilde = (comp, options) => {
     if (isX(M)) {
       ret = ''
     } else if (isX(m)) {
-      ret = `>=${M}.0.0 <${+M + 1}.0.0-0`
+      ret = `>=${M}.0.0${z} <${+M + 1}.0.0-0`
     } else if (isX(p)) {
       // ~1.2 == >=1.2.0 <1.3.0-0
-      ret = `>=${M}.${m}.0 <${M}.${+m + 1}.0-0`
+      ret = `>=${M}.${m}.0${z} <${M}.${+m + 1}.0-0`
     } else if (pr) {
       debug('replaceTilde pr', pr)
       ret = `>=${M}.${m}.${p}-${pr
diff --git a/test/fixtures/range-include.js b/test/fixtures/range-include.js
index ab2b836c..3df851b8 100644
--- a/test/fixtures/range-include.js
+++ b/test/fixtures/range-include.js
@@ -112,6 +112,13 @@ module.exports = [
   ['2.x', '2.1.0-pre.0', { includePrerelease: true }],
   ['1.1.x', '1.1.0-a', { includePrerelease: true }],
   ['1.1.x', '1.1.1-a', { includePrerelease: true }],
+  // tilde ranges are documented as equivalent to the matching x-range,
+  // so with includePrerelease they must accept the same prereleases. #512
+  ['~1.1', '1.1.0-a', { includePrerelease: true }],
+  ['~1.1.x', '1.1.0-a', { includePrerelease: true }],
+  ['~1.1', '1.1.1-a', { includePrerelease: true }],
+  ['~2', '2.0.0-pre.0', { includePrerelease: true }],
+  ['~2.x', '2.0.0-pre.0', { includePrerelease: true }],
   ['*', '1.0.0-rc1', { includePrerelease: true }],
   ['^1.0.0-0', '1.0.1-rc1', { includePrerelease: true }],
   ['^1.0.0-rc2', '1.0.1-rc1', { includePrerelease: true }],
diff --git a/test/fixtures/range-parse.js b/test/fixtures/range-parse.js
index c99ca40a..1c69c96d 100644
--- a/test/fixtures/range-parse.js
+++ b/test/fixtures/range-parse.js
@@ -57,6 +57,18 @@ module.exports = [
   ['~> 1', '>=1.0.0 <2.0.0-0'],
   ['~1.0', '>=1.0.0 <1.1.0-0'],
   ['~ 1.0', '>=1.0.0 <1.1.0-0'],
+  // tilde with includePrerelease must lower-bound at -0 just like the
+  // equivalent x-range (e.g. ~1.2 is documented as the same as 1.2.x),
+  // so that prereleases such as 1.2.0-rc match. See #512.
+  ['~1', '>=1.0.0-0 <2.0.0-0', { includePrerelease: true }],
+  ['~1.x', '>=1.0.0-0 <2.0.0-0', { includePrerelease: true }],
+  ['~1.2', '>=1.2.0-0 <1.3.0-0', { includePrerelease: true }],
+  ['~1.2.x', '>=1.2.0-0 <1.3.0-0', { includePrerelease: true }],
+  ['~0.0', '<0.1.0-0', { includePrerelease: true }],
+  // a fully-specified tilde keeps its exact lower bound (matches caret),
+  // and an explicit prerelease is preserved as-is
+  ['~1.2.3', '>=1.2.3 <1.3.0-0', { includePrerelease: true }],
+  ['~1.2.3-beta.4', '>=1.2.3-beta.4 <1.3.0-0', { includePrerelease: true }],
   ['^0', '<1.0.0-0'],
   ['^ 1', '>=1.0.0 <2.0.0-0'],
   ['^0.1', '>=0.1.0 <0.2.0-0'],