diff --git a/Library/Homebrew/extend/os/linux/hardware/cpu.rb b/Library/Homebrew/extend/os/linux/hardware/cpu.rb
index 99ede69a0b..67dd402a1c 100644
--- a/Library/Homebrew/extend/os/linux/hardware/cpu.rb
+++ b/Library/Homebrew/extend/os/linux/hardware/cpu.rb
@@ -3,17 +3,12 @@
 module Hardware
   class CPU
     class << self
-      OPTIMIZATION_FLAGS_LINUX = {
-        native:  "-march=#{Homebrew::EnvConfig.arch}",
-        nehalem: "-march=nehalem",
-        core2:   "-march=core2",
-        core:    "-march=prescott",
-        armv6:   "-march=armv6",
-        armv8:   "-march=armv8-a",
-      }.freeze
-
       def optimization_flags
-        OPTIMIZATION_FLAGS_LINUX
+        @optimization_flags ||= begin
+          flags = generic_optimization_flags.dup
+          flags[:native] = arch_flag(Homebrew::EnvConfig.arch)
+          flags
+        end
       end
 
       def cpuinfo
diff --git a/Library/Homebrew/extend/os/linux/install.rb b/Library/Homebrew/extend/os/linux/install.rb
index 7efbff87da..694e2a5cc5 100644
--- a/Library/Homebrew/extend/os/linux/install.rb
+++ b/Library/Homebrew/extend/os/linux/install.rb
@@ -14,6 +14,19 @@ module Homebrew
       "/system/bin/linker",
     ].freeze
 
+    def check_cpu
+      return if (Hardware::CPU.intel? && Hardware::CPU.is_64_bit?) || Hardware::CPU.arm?
+
+      message = "Sorry, Homebrew does not support your computer's CPU architecture!"
+      if Hardware::CPU.ppc64le?
+        message += <<~EOS
+          For OpenPOWER Linux (PPC64LE) support, see:
+            #{Formatter.url("https://github.com/homebrew-ppc64le/brew")}
+        EOS
+      end
+      abort message
+    end
+
     def symlink_ld_so
       brew_ld_so = HOMEBREW_PREFIX/"lib/ld.so"
       return if brew_ld_so.readable?
diff --git a/Library/Homebrew/hardware.rb b/Library/Homebrew/hardware.rb
index 9c9c00ce0d..9bee7f7d9c 100644
--- a/Library/Homebrew/hardware.rb
+++ b/Library/Homebrew/hardware.rb
@@ -7,28 +7,29 @@ module Hardware
     INTEL_32BIT_ARCHS = [:i386].freeze
     INTEL_64BIT_ARCHS = [:x86_64].freeze
     PPC_32BIT_ARCHS   = [:ppc, :ppc32, :ppc7400, :ppc7450, :ppc970].freeze
-    PPC_64BIT_ARCHS   = [:ppc64].freeze
+    PPC_64BIT_ARCHS   = [:ppc64, :ppc64le, :ppc970].freeze
 
     class << self
-      OPTIMIZATION_FLAGS = {
-        native:  "-march=native",
-        nehalem: "-march=nehalem",
-        core2:   "-march=core2",
-        core:    "-march=prescott",
-        armv6:   "-march=armv6",
-        armv8:   "-march=armv8-a",
-      }.freeze
-
       def optimization_flags
-        OPTIMIZATION_FLAGS
+        @optimization_flags ||= {
+          native:  arch_flag("native"),
+          nehalem: "-march=nehalem",
+          core2:   "-march=core2",
+          core:    "-march=prescott",
+          armv6:   "-march=armv6",
+          armv8:   "-march=armv8-a",
+          ppc64:   "-mcpu=powerpc64",
+          ppc64le: "-mcpu=powerpc64le",
+        }.freeze
       end
+      alias generic_optimization_flags optimization_flags
 
       def arch_32_bit
         if arm?
           :arm
         elsif intel?
           :i386
-        elsif ppc?
+        elsif ppc32?
           :ppc32
         else
           :dunno
@@ -40,7 +41,9 @@ module Hardware
           :arm64
         elsif intel?
           :x86_64
-        elsif ppc?
+        elsif ppc64le?
+          :ppc64le
+        elsif ppc64?
           :ppc64
         else
           :dunno
@@ -66,7 +69,7 @@ module Hardware
         case RUBY_PLATFORM
         when /x86_64/, /i\d86/ then :intel
         when /arm/, /aarch64/ then :arm
-        when /ppc\d+/ then :ppc
+        when /ppc|powerpc/ then :ppc
         else :dunno
         end
       end
@@ -85,7 +88,7 @@ module Hardware
 
       def bits
         @bits ||= case RUBY_PLATFORM
-        when /x86_64/, /ppc64/, /aarch64|arm64/ then 64
+        when /x86_64/, /ppc64|powerpc64/, /aarch64|arm64/ then 64
         when /i\d86/, /ppc/, /arm/ then 32
         end
       end
@@ -110,10 +113,30 @@ module Hardware
         type == :ppc
       end
 
+      def ppc32?
+        ppc? && is_32_bit?
+      end
+
+      def ppc64le?
+        ppc? && is_64_bit? && little_endian?
+      end
+
+      def ppc64?
+        ppc? && is_64_bit? && big_endian?
+      end
+
       def arm?
         type == :arm
       end
 
+      def little_endian?
+        !big_endian?
+      end
+
+      def big_endian?
+        [1].pack("I") == [1].pack("N")
+      end
+
       def features
         []
       end
@@ -121,6 +144,12 @@ module Hardware
       def feature?(name)
         features.include?(name)
       end
+
+      def arch_flag(arch)
+        return "-mcpu=#{arch}" if ppc?
+
+        "-march=#{arch}"
+      end
     end
   end
 
diff --git a/Library/Homebrew/install.rb b/Library/Homebrew/install.rb
index 86d63161f3..4a3f031327 100644
--- a/Library/Homebrew/install.rb
+++ b/Library/Homebrew/install.rb
@@ -10,14 +10,16 @@ module Homebrew
     module_function
 
     def check_cpu
-      case Hardware::CPU.type
-      when :ppc
-        abort <<~EOS
-          Sorry, Homebrew does not support your computer's CPU architecture.
-          For PPC support, see:
+      return if Hardware::CPU.intel? && Hardware::CPU.is_64_bit?
+
+      message = "Sorry, Homebrew does not support your computer's CPU architecture!"
+      if Hardware::CPU.ppc?
+        message += <<~EOS
+          For PowerPC Mac (PPC32/PPC64BE) support, see:
             #{Formatter.url("https://github.com/mistydemeo/tigerbrew")}
         EOS
       end
+      abort message
     end
 
     def attempt_directory_creation