diff --git a/app/vmselect/promql/binary_op.go b/app/vmselect/promql/binary_op.go
index 7bde1cab5..609ce1020 100644
--- a/app/vmselect/promql/binary_op.go
+++ b/app/vmselect/promql/binary_op.go
@@ -416,10 +416,25 @@ func binaryOpIfnot(left, right float64) float64 {
 }
 
 func binaryOpEq(left, right float64) bool {
+	// Special handling for nan == nan.
+	// See https://github.com/VictoriaMetrics/VictoriaMetrics/issues/150 .
+	if math.IsNaN(left) {
+		return math.IsNaN(right)
+	}
+
 	return left == right
 }
 
 func binaryOpNeq(left, right float64) bool {
+	// Special handling for comparison with nan.
+	// See https://github.com/VictoriaMetrics/VictoriaMetrics/issues/150 .
+	if math.IsNaN(left) {
+		return !math.IsNaN(right)
+	}
+	if math.IsNaN(right) {
+		return true
+	}
+
 	return left != right
 }
 
diff --git a/app/vmselect/promql/lexer.go b/app/vmselect/promql/lexer.go
index 6be24bec5..8dfe23208 100644
--- a/app/vmselect/promql/lexer.go
+++ b/app/vmselect/promql/lexer.go
@@ -149,12 +149,6 @@ func scanString(s string) (string, error) {
 }
 
 func scanPositiveNumber(s string) (string, error) {
-	if strings.HasPrefix(s, "Inf") {
-		return "Inf", nil
-	}
-	if strings.HasPrefix(s, "NaN") {
-		return "NaN", nil
-	}
 	// Scan integer part. It may be empty if fractional part exists.
 	i := 0
 	for i < len(s) && isDecimalChar(s[i]) {
@@ -333,6 +327,14 @@ func scanTagFilterOpPrefix(s string) int {
 	return -1
 }
 
+func isInfOrNaN(s string) bool {
+	if len(s) != 3 {
+		return false
+	}
+	s = strings.ToLower(s)
+	return s == "inf" || s == "nan"
+}
+
 func isOffset(s string) bool {
 	s = strings.ToLower(s)
 	return s == "offset"
@@ -361,7 +363,7 @@ func isPositiveNumberPrefix(s string) bool {
 
 	// Check for .234 numbers
 	if s[0] != '.' || len(s) < 2 {
-		return strings.HasPrefix(s, "Inf") || strings.HasPrefix(s, "NaN")
+		return false
 	}
 	return isDecimalChar(s[1])
 }
diff --git a/app/vmselect/promql/parser.go b/app/vmselect/promql/parser.go
index 6c72690d0..b2511727e 100644
--- a/app/vmselect/promql/parser.go
+++ b/app/vmselect/promql/parser.go
@@ -373,7 +373,7 @@ func (p *parser) parseSingleExpr() (expr, error) {
 }
 
 func (p *parser) parseSingleExprWithoutRollupSuffix() (expr, error) {
-	if isPositiveNumberPrefix(p.lex.Token) {
+	if isPositiveNumberPrefix(p.lex.Token) || isInfOrNaN(p.lex.Token) {
 		return p.parsePositiveNumberExpr()
 	}
 	if isStringPrefix(p.lex.Token) {
@@ -417,7 +417,7 @@ func (p *parser) parseSingleExprWithoutRollupSuffix() (expr, error) {
 }
 
 func (p *parser) parsePositiveNumberExpr() (*numberExpr, error) {
-	if !isPositiveNumberPrefix(p.lex.Token) {
+	if !isPositiveNumberPrefix(p.lex.Token) && !isInfOrNaN(p.lex.Token) {
 		return nil, fmt.Errorf(`positiveNumberExpr: unexpected token %q; want "number"`, p.lex.Token)
 	}
 
diff --git a/app/vmselect/promql/parser_test.go b/app/vmselect/promql/parser_test.go
index cc90abf19..1ef8554cb 100644
--- a/app/vmselect/promql/parser_test.go
+++ b/app/vmselect/promql/parser_test.go
@@ -170,14 +170,34 @@ func TestParsePromQLSuccess(t *testing.T) {
 	another(`-.2`, `-0.2`)
 	another(`-.2E-2`, `-0.002`)
 	same(`NaN`)
+	another(`nan`, `NaN`)
+	another(`NAN`, `NaN`)
+	another(`nAN`, `NaN`)
 	another(`Inf`, `+Inf`)
+	another(`INF`, `+Inf`)
+	another(`inf`, `+Inf`)
 	another(`+Inf`, `+Inf`)
 	another(`-Inf`, `-Inf`)
+	another(`-inF`, `-Inf`)
 
 	// binaryOpExpr
-	another(`NaN + 2 *3 * Inf`, `NaN`)
-	another(`Inf - Inf`, `NaN`)
-	another(`Inf + Inf`, `+Inf`)
+	another(`nan == nan`, `NaN`)
+	another(`nan ==bool nan`, `1`)
+	another(`nan !=bool nan`, `0`)
+	another(`nan !=bool 2`, `1`)
+	another(`2 !=bool nan`, `1`)
+	another(`nan >bool nan`, `0`)
+	another(`nan <bool nan`, `0`)
+	another(`1 ==bool nan`, `0`)
+	another(`NaN !=bool 1`, `1`)
+	another(`inf >=bool 2`, `1`)
+	another(`-1 >bool -inf`, `1`)
+	another(`-1 <bool -inf`, `0`)
+	another(`nan + 2 *3 * inf`, `NaN`)
+	another(`INF - Inf`, `NaN`)
+	another(`Inf + inf`, `+Inf`)
+	another(`1/0`, `+Inf`)
+	another(`0/0`, `NaN`)
 	another(`-m`, `0 - m`)
 	same(`m + ignoring () n[5m]`)
 	another(`M + IGNORING () N[5m]`, `M + ignoring () N[5m]`)