diff --git a/lib/select.c b/lib/select.c
index d91b20a..abb124a 100644
--- a/lib/select.c
+++ b/lib/select.c
@@ -22,6 +22,8 @@
 
 #include "curl_setup.h"
 
+#include <limits.h>
+
 #ifdef HAVE_SYS_SELECT_H
 #include <sys/select.h>
 #elif defined(HAVE_UNISTD_H)
@@ -50,11 +52,9 @@
 #include "urldata.h"
 #include "connect.h"
 #include "select.h"
+#include "timeval.h"
 #include "warnless.h"
 
-/* Convenience local macros */
-#define ELAPSED_MS() (int)Curl_timediff(Curl_now(), initial_tv)
-
 /*
  * Internal function used for waiting a specific amount of ms
  * in Curl_socket_check() and Curl_poll() when no file descriptor
@@ -71,7 +71,7 @@
  *   -1 = system call error, invalid timeout value, or interrupted
  *    0 = specified timeout has elapsed
  */
-int Curl_wait_ms(int timeout_ms)
+int Curl_wait_ms(timediff_t timeout_ms)
 {
   int r = 0;
 
@@ -83,16 +83,44 @@
   }
 #if defined(MSDOS)
   delay(timeout_ms);
-#elif defined(USE_WINSOCK)
-  Sleep(timeout_ms);
+#elif defined(WIN32)
+  /* prevent overflow, timeout_ms is typecast to ULONG/DWORD. */
+#if TIMEDIFF_T_MAX >= ULONG_MAX
+  if(timeout_ms >= ULONG_MAX)
+    timeout_ms = ULONG_MAX-1;
+    /* don't use ULONG_MAX, because that is equal to INFINITE */
+#endif
+  Sleep((ULONG)timeout_ms);
 #else
 #if defined(HAVE_POLL_FINE)
-  r = poll(NULL, 0, timeout_ms);
+  /* prevent overflow, timeout_ms is typecast to int. */
+#if TIMEDIFF_T_MAX > INT_MAX
+  if(timeout_ms > INT_MAX)
+    timeout_ms = INT_MAX;
+#endif
+  r = poll(NULL, 0, (int)timeout_ms);
 #else
   {
     struct timeval pending_tv;
-    pending_tv.tv_sec = timeout_ms / 1000;
-    pending_tv.tv_usec = (timeout_ms % 1000) * 1000;
+    timediff_t tv_sec = timeout_ms / 1000;
+    timediff_t tv_usec = (timeout_ms % 1000) * 1000; /* max=999999 */
+#ifdef HAVE_SUSECONDS_T
+#if TIMEDIFF_T_MAX > TIME_T_MAX
+    /* tv_sec overflow check in case time_t is signed */
+    if(tv_sec > TIME_T_MAX)
+      tv_sec = TIME_T_MAX;
+#endif
+    pending_tv.tv_sec = (time_t)tv_sec;
+    pending_tv.tv_usec = (suseconds_t)tv_usec;
+#else
+#if TIMEDIFF_T_MAX > INT_MAX
+    /* tv_sec overflow check in case time_t is signed */
+    if(tv_sec > INT_MAX)
+      tv_sec = INT_MAX;
+#endif
+    pending_tv.tv_sec = (int)tv_sec;
+    pending_tv.tv_usec = (int)tv_usec;
+#endif
     r = select(0, NULL, NULL, NULL, &pending_tv);
   }
 #endif /* HAVE_POLL_FINE */
@@ -113,44 +141,60 @@
  *    0 = timeout
  *    N = number of signalled file descriptors
  */
-int Curl_select(curl_socket_t maxfd,
-                fd_set *fds_read,
-                fd_set *fds_write,
-                fd_set *fds_err,
-                time_t timeout_ms)     /* milliseconds to wait */
+int Curl_select(curl_socket_t maxfd,   /* highest socket number */
+                fd_set *fds_read,      /* sockets ready for reading */
+                fd_set *fds_write,     /* sockets ready for writing */
+                fd_set *fds_err,       /* sockets with errors */
+                timediff_t timeout_ms) /* milliseconds to wait */
 {
   struct timeval pending_tv;
   struct timeval *ptimeout;
-  int pending_ms;
   int r;
 
-#if SIZEOF_TIME_T != SIZEOF_INT
-  /* wrap-around precaution */
-  if(timeout_ms >= INT_MAX)
-    timeout_ms = INT_MAX;
-#endif
-
 #ifdef USE_WINSOCK
   /* WinSock select() can't handle zero events.  See the comment below. */
   if((!fds_read || fds_read->fd_count == 0) &&
      (!fds_write || fds_write->fd_count == 0) &&
      (!fds_err || fds_err->fd_count == 0)) {
-    r = Curl_wait_ms((int)timeout_ms);
+    r = Curl_wait_ms(timeout_ms);
     return r;
   }
 #endif
 
   ptimeout = &pending_tv;
-
   if(timeout_ms < 0) {
     ptimeout = NULL;
   }
   else if(timeout_ms > 0) {
-    pending_ms = (int)timeout_ms;
-    pending_tv.tv_sec = pending_ms / 1000;
-    pending_tv.tv_usec = (pending_ms % 1000) * 1000;
+    timediff_t tv_sec = timeout_ms / 1000;
+    timediff_t tv_usec = (timeout_ms % 1000) * 1000; /* max=999999 */
+#ifdef HAVE_SUSECONDS_T
+#if TIMEDIFF_T_MAX > TIME_T_MAX
+    /* tv_sec overflow check in case time_t is signed */
+    if(tv_sec > TIME_T_MAX)
+      tv_sec = TIME_T_MAX;
+#endif
+    pending_tv.tv_sec = (time_t)tv_sec;
+    pending_tv.tv_usec = (suseconds_t)tv_usec;
+#elif defined(WIN32) /* maybe also others in the future */
+#if TIMEDIFF_T_MAX > LONG_MAX
+    /* tv_sec overflow check on Windows there we know it is long */
+    if(tv_sec > LONG_MAX)
+      tv_sec = LONG_MAX;
+#endif
+    pending_tv.tv_sec = (long)tv_sec;
+    pending_tv.tv_usec = (long)tv_usec;
+#else
+#if TIMEDIFF_T_MAX > INT_MAX
+    /* tv_sec overflow check in case time_t is signed */
+    if(tv_sec > INT_MAX)
+      tv_sec = INT_MAX;
+#endif
+    pending_tv.tv_sec = (int)tv_sec;
+    pending_tv.tv_usec = (int)tv_usec;
+#endif
   }
-  else if(!timeout_ms) {
+  else {
     pending_tv.tv_sec = 0;
     pending_tv.tv_usec = 0;
   }
@@ -201,11 +245,10 @@
 int Curl_socket_check(curl_socket_t readfd0, /* two sockets to read from */
                       curl_socket_t readfd1,
                       curl_socket_t writefd, /* socket to write to */
-                      timediff_t timeout_ms)     /* milliseconds to wait */
+                      timediff_t timeout_ms) /* milliseconds to wait */
 {
 #ifdef HAVE_POLL_FINE
   struct pollfd pfd[3];
-  int pending_ms;
   int num;
 #else
   fd_set fds_read;
@@ -216,16 +259,10 @@
   int r;
   int ret;
 
-#if SIZEOF_TIME_T != SIZEOF_INT
-  /* wrap-around precaution */
-  if(timeout_ms >= INT_MAX)
-    timeout_ms = INT_MAX;
-#endif
-
   if((readfd0 == CURL_SOCKET_BAD) && (readfd1 == CURL_SOCKET_BAD) &&
      (writefd == CURL_SOCKET_BAD)) {
     /* no sockets, just wait */
-    r = Curl_wait_ms((int)timeout_ms);
+    r = Curl_wait_ms(timeout_ms);
     return r;
   }
 
@@ -256,18 +293,9 @@
     num++;
   }
 
-  if(timeout_ms > 0)
-    pending_ms = (int)timeout_ms;
-  else if(timeout_ms < 0)
-    pending_ms = -1;
-  else
-    pending_ms = 0;
-  r = poll(pfd, num, pending_ms);
-
-  if(r < 0)
-    return -1;
-  if(r == 0)
-    return 0;
+  r = Curl_poll(pfd, num, timeout_ms);
+  if(r <= 0)
+    return r;
 
   ret = 0;
   num = 0;
@@ -333,7 +361,7 @@
      curl_socket_t is unsigned in such cases and thus -1 is the largest
      value).
   */
-  r = Curl_select(maxfd, &fds_read, &fds_write, &fds_err, (time_t)timeout_ms);
+  r = Curl_select(maxfd, &fds_read, &fds_write, &fds_err, timeout_ms);
 
   if(r < 0)
     return -1;
@@ -379,7 +407,7 @@
  *    0 = timeout
  *    N = number of structures with non zero revent fields
  */
-int Curl_poll(struct pollfd ufds[], unsigned int nfds, int timeout_ms)
+int Curl_poll(struct pollfd ufds[], unsigned int nfds, timediff_t timeout_ms)
 {
 #ifdef HAVE_POLL_FINE
   int pending_ms;
@@ -402,6 +430,7 @@
     }
   }
   if(fds_none) {
+    /* no sockets, just wait */
     r = Curl_wait_ms(timeout_ms);
     return r;
   }
@@ -413,8 +442,13 @@
 
 #ifdef HAVE_POLL_FINE
 
+  /* prevent overflow, timeout_ms is typecast to int. */
+#if TIMEDIFF_T_MAX > INT_MAX
+  if(timeout_ms > INT_MAX)
+    timeout_ms = INT_MAX;
+#endif
   if(timeout_ms > 0)
-    pending_ms = timeout_ms;
+    pending_ms = (int)timeout_ms;
   else if(timeout_ms < 0)
     pending_ms = -1;
   else