diff --git a/NEWS.md b/NEWS.md
index 3c60946abd..e72ea27667 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -251,6 +251,8 @@
 
 36. `DT[id==1, DT2[.SD, on="id"]]` (i.e. joining from `.SD` in `j`) could incorrectly fail in some cases due to `.SD` being locked, [#1926](https://github.com/Rdatatable/data.table/issues/1926). Thanks @franknarf1 for the report and for diligently tracking use cases for almost 3 years!
 
+37. `as.IDate.POSIXct` returned `NA` for UTC times before Dec 1901 and after Jan 2038, [#3780](https://github.com/Rdatatable/data.table/issues/3780). Thanks @gschett for the report.
+
 #### NOTES
 
 1. `rbindlist`'s `use.names="check"` now emits its message for automatic column names (`"V[0-9]+"`) too, [#3484](https://github.com/Rdatatable/data.table/pull/3484). See news item 5 of v1.12.2 below.
diff --git a/R/IDateTime.R b/R/IDateTime.R
index 8e03631066..c0e31bc248 100644
--- a/R/IDateTime.R
+++ b/R/IDateTime.R
@@ -35,7 +35,7 @@ as.IDate.Date = function(x, ...) {
 as.IDate.POSIXct = function(x, tz = attr(x, "tzone", exact=TRUE), ...) {
   if (is.null(tz)) tz = "UTC"
   if (tz %chin% c("UTC", "GMT")) {
-    (setattr(as.integer(x) %/% 86400L, "class", c("IDate", "Date")))  # %/% returns new object so can use setattr() on it; wrap with () to return visibly
+    (setattr(as.integer(as.numeric(x) %/% 86400L), "class", c("IDate", "Date")))  # %/% returns new object so can use setattr() on it; wrap with () to return visibly
   } else
     as.IDate(as.Date(x, tz = tz, ...))
 }
@@ -305,7 +305,7 @@ as.POSIXlt.ITime = function(x, ...) {
 second  = function(x) {
   if (inherits(x, 'POSIXct') && identical(attr(x, 'tzone', exact=TRUE), 'UTC')) {
     # if we know the object is in UTC, can calculate the hour much faster
-    as.integer(x) %% 60L
+    as.integer(as.numeric(x) %% 60L)
   } else {
     as.integer(as.POSIXlt(x)$sec)
   }
@@ -313,7 +313,7 @@ second  = function(x) {
 minute  = function(x) {
   if (inherits(x, 'POSIXct') && identical(attr(x, 'tzone', exact=TRUE), 'UTC')) {
     # ever-so-slightly faster than x %% 3600L %/% 60L
-    as.integer(x) %/% 60L %% 60L
+    as.integer(as.numeric(x) %/% 60L %% 60L)
   } else {
     as.POSIXlt(x)$min
   }
@@ -321,7 +321,7 @@ minute  = function(x) {
 hour = function(x) {
   if (inherits(x, 'POSIXct') && identical(attr(x, 'tzone', exact=TRUE), 'UTC')) {
     # ever-so-slightly faster than x %% 86400L %/% 3600L
-    as.integer(x) %/% 3600L %% 24L
+    as.integer(as.numeric(x) %/% 3600L %% 24L)
   } else {
     as.POSIXlt(x)$hour
   }
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index 8a308c19c8..736ff800bf 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -15827,6 +15827,14 @@ df1 = data.table(a=1:5, b=c(0, 0, 1, 0, 2))
 df2 = data.table(c=c(1, 1, 2, 2, 3), d=c(3, 4, 3, 5, 4))
 test(2092.3, copy(df2)[ , s := df1[.SD, on=.(a >= c, a <= d), sum(b), by=.EACHI]$V1],
      df2[ , s := c(1, 1, 1, 3, 1)])
+     
+# POSIXct overflow to NA before 1901 and after 2038, #3780
+date=as.POSIXct("1900-01-01", tz="UTC")
+test(2093.1, as.IDate(date), as.IDate(-25567L))
+test(2093.2, hour(date), 0L)
+test(2093.3, minute(date), 0L)
+test(2093.4, second(date), 0L)
+
 
 ###################################
 #  Add new tests above this line  #